# line start with '#' is a comment line, blank line can be skipped by code
# Format of this file is
# spgid      space-group-number
# sspgname   short-Hermann-Mauguin-symbol 
# fspgname   full-Hermann-Mauguin-symbol
# pgname     point-group-symbol
# crysym     crystal-system-name
# xyzasu     real-space-ASU-description
# primoper   symmetry-operations
# centoper   centering-operations
# note: The identity transformation should always be the first symm. oper.
 
spgid 1
sspgname  P 1
fspgname  P 1
pgname    1
crysym    triclinic
xyzasu    0<=x<1; 0<=y<1; 0<=z<1
primoper  x,y,z
centoper  x,y,z
endofdef  
                                                                 
spgid 1
sspgname  A 1
fspgname  A 1 1 1
pgname    1
crysym    triclinic
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<1
primoper  x,y,z
centoper  x,y,z
centoper  x,y+1/2,z+1/2
endofdef 

spgid 2
sspgname  P -1
fspgname  P -1
pgname    -1
crysym    triclinic
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,-z
centoper  x,y,z
endofdef 

spgid 2
sspgname  P 1-
fspgname  P 1-
pgname    -1
crysym    triclinic
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,-z
centoper  x,y,z
endofdef

spgid 3
sspgname  P 2
fspgname  P 2
pgname    2
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/2
primoper  x,y,z
primoper  -x,y,-z
centoper  x,y,z
endofdef
 
spgid 3
sspgname  P 2
fspgname  P 1 2 1
pgname    2
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/2
primoper  x,y,z
primoper  -x,y,-z
centoper  x,y,z
endofdef  

spgid 3
sspgname  P 2
fspgname  P 1 1 2
pgname    2
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<1
primoper  x,y,z
primoper  -x,-y,z
centoper  x,y,z
endofdef  

spgid 4
sspgname  P 21
fspgname  P 21
pgname    2
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/2
primoper  x,y,z
primoper  -x,y+1/2,-z
centoper  x,y,z
endofdef

spgid 4
sspgname  P 21
fspgname  P 1 21 1
pgname    2
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/2
primoper  x,y,z
primoper  -x,y+1/2,-z
centoper  x,y,z
endofdef  

spgid 4
sspgname  P 21
fspgname  P 1 1 21
pgname    2
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z+1/2
centoper  x,y,z
endofdef  

spgid 5
sspgname  C 2
fspgname  C 2
pgname    2
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,y,-z
centoper  x,y,z
centoper  x+1/2,y+1/2,z
endofdef

spgid 5
sspgname  C 2
fspgname  C 1 2 1
pgname    2
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,y,-z
centoper  x,y,z
centoper  x+1/2,y+1/2,z
endofdef  

spgid 5
sspgname  A 2
fspgname  A 1 2 1
pgname    2
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/4
primoper  x,y,z
primoper  -x,y,-z
centoper  x,y,z
centoper  x,y+1/2,z+1/2
endofdef  

spgid 5
sspgname  C 2
fspgname  I 1 2 1
pgname    2
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/4
primoper  x,y,z
primoper  -x,y,-z
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef  

spgid 5
sspgname  C 2
fspgname  A 1 1 2
pgname    2
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
centoper  x,y,z
centoper  x,y+1/2,z+1/2
endofdef  

spgid 5
sspgname  B 2
fspgname  B 1 1 2
pgname    2
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
centoper  x,y,z
centoper  x+1/2,y,z+1/2
endofdef  

spgid 5
sspgname  C 2
fspgname  I 1 1 2
pgname    2
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef  

spgid  5
sspgname  C 21 
fspgname  C 1 21 1
pgname    2 
crysym    monoclinic
xyzasu    0<=x<=1/2; 0<=y<1; 0<=z<=1/2
primoper  x,y,z
primoper  -x,y+1/2,-z
centoper  x,y,z
centoper  x+1/2,y+1/2,z
endofdef

spgid 6
sspgname  P m
fspgname  P 1 m 1 
pgname    m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<1
primoper  x,y,z
primoper  x,-y,z
centoper  x,y,z
endofdef  

spgid 6
sspgname  P m
fspgname  P 1 1 m 
pgname    m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/2
primoper  x,y,z
primoper  x,y,-z
centoper  x,y,z
endofdef  

spgid 7
sspgname  P c
fspgname  P 1 c 1 
pgname    m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/2
primoper  x,y,z
primoper  x,-y,z+1/2
centoper  x,y,z
endofdef  

spgid 7
sspgname  P c
fspgname  P 1 n 1 
pgname    m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/2
primoper  x,y,z
primoper  x+1/2,-y,z+1/2
centoper  x,y,z
endofdef  

spgid 7
sspgname  P c
fspgname  P 1 a 1 
pgname    m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<1
primoper  x,y,z
primoper  x+1/2,-y,z
centoper  x,y,z
endofdef  

spgid 7
sspgname  P c
fspgname  P 1 1 a 
pgname    m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/2
primoper  x,y,z
primoper  x+1/2,y,-z
centoper  x,y,z
endofdef  

spgid 7
sspgname  P c
fspgname  P 1 1 n 
pgname    m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/2
primoper  x,y,z
primoper  x+1/2,y+1/2,-z
centoper  x,y,z
endofdef  

spgid 7
sspgname  P c
fspgname  P 1 1 b
pgname    m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/2
primoper  x,y,z
primoper  x,y+1/2,-z
centoper  x,y,z
endofdef  

spgid 8
sspgname  C m
fspgname  C 1 m 1 
pgname    m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<=1/4; 0<=z<1
primoper  x,y,z
primoper  x,-y,z
centoper  x,y,z
centoper  x+1/2,y+1/2,z
endofdef  

spgid 8
sspgname  C m
fspgname  A 1 m 1 
pgname    m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  x,-y,z
centoper  x,y,z
centoper  x,y+1/2,z+1/2
endofdef  

spgid 8
sspgname  C m
fspgname  I 1 m 1 
pgname    m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  x,-y,z
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef  

spgid 8
sspgname  C m
fspgname  A 1 1 m 
pgname    m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/4
primoper  x,y,z
primoper  x,y,-z
centoper  x,y,z
centoper  x,y+1/2,z+1/2
endofdef  

spgid 8
sspgname  C m
fspgname  B 1 1 m 
pgname    m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/4
primoper  x,y,z
primoper  x,y,-z
centoper  x,y,z
centoper  x+1/2,y,z+1/2
endofdef  

spgid 8
sspgname  C m
fspgname  I 1 1 m 
pgname    m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/4
primoper  x,y,z
primoper  x,y,-z
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef  

spgid 9
sspgname  C c
fspgname  C 1 c 1 
pgname    m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  x,-y,z+1/2
centoper  x,y,z
centoper  x+1/2,y+1/2,z
endofdef  

spgid 9
sspgname  C c
fspgname  A 1 n 1 
pgname    m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/2
primoper  x,y,z
primoper  x+1/2,-y,z+1/2
centoper  x,y,z
centoper  x,y+1/2,z+1/2
endofdef  

spgid 9
sspgname  C c
fspgname  I 1 a 1 
pgname    m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  x+1/2,-y,z
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef  

spgid 9
sspgname  C c
fspgname  A 1 1 a
pgname    m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/4
primoper  x,y,z
primoper  x+1/2,y,-z
centoper  x,y,z
centoper  x,y+1/2,z+1/2
endofdef  

spgid 9
sspgname  C c
fspgname  B 1 1 n
pgname    m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/4
primoper  x,y,z
primoper  x+1/2,y+1/2,-z
centoper  x,y,z
centoper  x+1/2,y,z+1/2
endofdef  

spgid 9
sspgname  C c
fspgname  I 1 1 b 
pgname    m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/4
primoper  x,y,z
primoper  x,y+1/2,-z
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef  

spgid  10
sspgname  P 2/m 
fspgname  P 1 2/m 1
pgname    2/m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,y,-z
primoper  -x,-y,-z
primoper  x,-y,z
centoper  x,y,z
endofdef

spgid  10
sspgname  P 2/m 
fspgname  P 1 1 2/m
pgname    2/m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  -x,-y,-z
primoper  x,y,-z
centoper  x,y,z
endofdef

spgid  11
sspgname  P 21/m
fspgname  P 1 21/m 1
pgname    2/m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/2
primoper  x,y,z
primoper  -x,y+1/2,-z
primoper  -x,-y,-z
primoper  x,-y+1/2,z
centoper  x,y,z
endofdef

spgid  11
sspgname  P 21/m
fspgname  P 1 1 21/m
pgname    2/m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z+1/2
primoper  -x,-y,-z
primoper  x,y,-z+1/2
centoper  x,y,z
endofdef


spgid  12
sspgname  C 2/m
fspgname  C 1 2/m 1
pgname    2/m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<=1/4; 0<=z<=1/2
primoper  x,y,z
primoper  -x,y,-z
primoper  -x,-y,-z
primoper  x,-y,z
centoper  x,y,z
centoper  x+1/2,y+1/2,z
endofdef


spgid  12
sspgname  C 2/m
fspgname  A 1 2/m 1
pgname    2/m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,y,-z
primoper  -x,-y,-z
primoper  x,-y,z
centoper  x,y,z
centoper  x,y+1/2,z+1/2
endofdef


spgid  12
sspgname  C 2/m
fspgname  I 1 2/m 1
pgname    2/m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,y,-z
primoper  -x,-y,-z
primoper  x,-y,z
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef


spgid  12
sspgname  C 2/m
fspgname  A 1 1 2/m
pgname    2/m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -x,-y,-z
primoper  x,y,-z
centoper  x,y,z
centoper  x,y+1/2,z+1/2
endofdef


spgid  12
sspgname  C 2/m
fspgname  B 1 1 2/m
pgname    2/m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -x,-y,-z
primoper  x,y,-z
centoper  x,y,z
centoper  x+1/2,y,z+1/2
endofdef


spgid  12
sspgname  C 2/m
fspgname  I 1 1 2/m
pgname    2/m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -x,-y,-z
primoper  x,y,-z
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef


spgid  13
sspgname  P 2/c
fspgname  P 1 2/c 1
pgname    2/m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/4
primoper  x,y,z
primoper  -x,y,-z+1/2
primoper  -x,-y,-z
primoper  x,-y,z+1/2
centoper  x,y,z
endofdef


spgid  13
sspgname  P 2/c
fspgname  P 1 2/n 1
pgname    2/m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/4
primoper  x,y,z
primoper  -x+1/2,y,-z+1/2
primoper  -x,-y,-z
primoper  x+1/2,-y,z+1/2
centoper  x,y,z
endofdef


spgid  13
sspgname  P 2/c
fspgname  P 1 2/a 1
pgname    2/m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x+1/2,y,-z
primoper  -x,-y,-z
primoper  x+1/2,-y,z
centoper  x,y,z
endofdef


spgid  13
sspgname  P 2/c
fspgname  P 1 1 2/a
pgname    2/m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x+1/2,-y,z
primoper  -x,-y,-z
primoper  x+1/2,y,-z
centoper  x,y,z
endofdef


spgid  13
sspgname  P 2/c
fspgname  P 1 1 2/n
pgname    2/m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/2
primoper  x,y,z
primoper  -x+1/2,-y+1/2,z
primoper  -x,-y,-z
primoper  x+1/2,y+1/2,-z
centoper  x,y,z
endofdef


spgid  13
sspgname  P 2/c
fspgname  P 1 1 2/b
pgname    2/m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y+1/2,z
primoper  -x,-y,-z
primoper  x,y+1/2,-z
centoper  x,y,z
endofdef


spgid  14
sspgname  P 21/c
fspgname  P 1 21/c 1
pgname    2/m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/4
primoper  x,y,z
primoper  -x,y+1/2,-z+1/2
primoper  -x,-y,-z
primoper  x,-y+1/2,z+1/2
centoper  x,y,z
endofdef


spgid  14
sspgname  P 21/c
fspgname  P 1 21/n 1
pgname    2/m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/4
primoper  x,y,z
primoper  -x+1/2,y+1/2,-z+1/2
primoper  -x,-y,-z
primoper  x+1/2,-y+1/2,z+1/2
centoper  x,y,z
endofdef


spgid  14
sspgname  P 21/c
fspgname  P 1 21/a 1
pgname    2/m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/2
primoper  x,y,z
primoper  -x+1/2,y+1/2,-z
primoper  -x,-y,-z
primoper  x+1/2,-y+1/2,z
centoper  x,y,z
endofdef


spgid  14
sspgname  P 21/c
fspgname  P 1 1 21/a
pgname    2/m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/4
primoper  x,y,z
primoper  -x+1/2,-y,z+1/2
primoper  -x,-y,-z
primoper  x+1/2,y,-z+1/2
centoper  x,y,z
endofdef


spgid  14
sspgname  P 21/c
fspgname  P 1 1 21/n
pgname    2/m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/4
primoper  x,y,z
primoper  -x+1/2,-y+1/2,z+1/2
primoper  -x,-y,-z
primoper  x+1/2,y+1/2,-z+1/2
centoper  x,y,z
endofdef


spgid  14
sspgname  P 21/c
fspgname  P 1 1 21/b
pgname    2/m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<=1; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y+1/2,z+1/2
primoper  -x,-y,-z
primoper  x,y+1/2,-z+1/2
centoper  x,y,z
endofdef


spgid  15
sspgname  C 2/c
fspgname  C 1 2/c 1
pgname    2/m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,y,-z+1/2
primoper  -x,-y,-z
primoper  x,-y,z+1/2
centoper  x,y,z
centoper  x+1/2,y+1/2,z
endofdef


spgid  15
sspgname  C 2/c
fspgname  A 1 2/n 1
pgname    2/m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/4
primoper  x,y,z
primoper  -x+1/2,y,-z+1/2
primoper  -x,-y,-z
primoper  x+1/2,-y,z+1/2
centoper  x,y,z
centoper  x,y+1/2,z+1/2
endofdef


spgid  15
sspgname  C 2/c
fspgname  I 1 2/a 1
pgname    2/m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x+1/2,y,-z
primoper  -x,-y,-z
primoper  x+1/2,-y,z
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef


spgid  15
sspgname  C 2/c
fspgname  A 1 1 2/a
pgname    2/m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x+1/2,-y,z
primoper  -x,-y,-z
primoper  x+1/2,y,-z
centoper  x,y,z
centoper  x,y+1/2,z+1/2
endofdef


spgid  15
sspgname  C 2/c
fspgname  B 1 1 2/n
pgname    2/m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/4
primoper  x,y,z
primoper  -x+1/2,-y+1/2,z
primoper  -x,-y,-z
primoper  x+1/2,y+1/2,-z
centoper  x,y,z
centoper  x+1/2,y,z+1/2
endofdef


spgid  15
sspgname  C 2/c
fspgname  I 1 1 2/b
pgname    2/m
crysym    monoclinic
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y+1/2,z
primoper  -x,-y,-z
primoper  x,y+1/2,-z
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef


spgid  16
sspgname  P 2 2 2 
fspgname  P 2 2 2
pgname    2 2 2 
crysym    orthorhombic 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  -x,y,-z
primoper  x,-y,-z
centoper  x,y,z
endofdef


spgid  17
sspgname  P 2 2 21 
fspgname  P 2 2 21
pgname    2 2 2 
crysym    orthorhombic 
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z+1/2
primoper  -x,y,-z+1/2
primoper  x,-y,-z
centoper  x,y,z
endofdef

spgid  18
sspgname  P 21 21 2 
fspgname  P 21 21 2
pgname    2 2 2 
crysym    orthorhombic 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  -x+1/2,y+1/2,-z
primoper  x+1/2,-y+1/2,-z
centoper  x,y,z
endofdef

spgid  18
sspgname  P 21 2 21 
fspgname  P 21 2 21
pgname    2 2 2 
crysym    orthorhombic 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,y,-z
primoper  -x+1/2,-y,z+1/2
primoper  x+1/2,-y,-z+1/2
centoper  x,y,z
endofdef

spgid  18
sspgname  P 21 21 2A 
fspgname  P 21 21 2A
pgname    2 2 2 
crysym    orthorhombic 
xyzasu    0<=x<=1/2; 0<=y<=1/2; 0<=z<1
primoper  x,y,z
primoper  -x+1/2,-y+1/2,z
primoper  x+1/2,-y,-z
primoper  -x,y+1/2,-z
centoper  x,y,z
endofdef

spgid  19
sspgname  P 21 21 21 
fspgname  P 21 21 21
pgname    2 2 2 
crysym    orthorhombic 
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/4
primoper  x,y,z
primoper  -x+1/2,-y,z+1/2
primoper  -x,y+1/2,-z+1/2
primoper  x+1/2,-y+1/2,-z
centoper  x,y,z
endofdef


spgid  20
sspgname  C 2 2 21 
fspgname  C 2 2 21
pgname    2 2 2 
crysym    orthorhombic 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z+1/2
primoper  -x,y,-z+1/2
primoper  x,-y,-z
centoper  x,y,z
centoper  x+1/2,y+1/2,z
endofdef

spgid  20
sspgname  B 2 21 2 
fspgname  B 2 21 2
pgname    2 2 2 
crysym    orthorhombic 
xyzasu    0<=x<=1/2; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y+1/2,z
primoper  -x,y+1/2,-z
primoper  -x,y,-z
centoper  x,y,z:
centoper  x+1/2,y,z+1/2
endofdef

spgid  21
sspgname  C 2 2 2 
fspgname  C 2 2 2
pgname    2 2 2 
crysym    orthorhombic 
xyzasu    0<=x<1; 0<=y<=1/4; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  -x,y,-z
primoper  x,-y,-z
centoper  x,y,z
centoper  x+1/2,y+1/2,z
endofdef


spgid  22
sspgname  F 2 2 2 
fspgname  F 2 2 2
pgname    2 2 2 
crysym    orthorhombic 
xyzasu    0<=x<1; 0<=y<=1/4; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -x,y,-z
primoper  x,-y,-z
centoper  x,y,z
centoper  x,y+1/2,z+1/2
centoper  x+1/2,y,z+1/2
centoper  x+1/2,y+1/2,z
endofdef


spgid  23
sspgname  I 2 2 2 
fspgname  I 2 2 2
pgname    2 2 2 
crysym    orthorhombic 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -x,y,-z
primoper  x,-y,-z
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef


spgid  24
sspgname  I 21 21 21 
fspgname  I 21 21 21
pgname    2 2 2 
crysym    orthorhombic 
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/4
primoper  x,y,z
primoper  -x+1/2,-y,z+1/2
primoper  -x,y+1/2,-z+1/2
primoper  x+1/2,-y+1/2,-z
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef


spgid  25
sspgname  P m m 2 
fspgname  P m m 2
pgname    m m 2 
crysym    orthorhombic 
xyzasu    0<=x<=1/2; 0<=y<=1/2; 0<=z<1
primoper  x,y,z
primoper  -x,-y,z
primoper  x,-y,z
primoper  -x,y,z
centoper  x,y,z
endofdef


spgid  26
sspgname  P m c 21 
fspgname  P m c 21
pgname    m m 2 
crysym    orthorhombic 
xyzasu    0<=x<=1/2; 0<=y<1; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z+1/2
primoper  x,-y,z+1/2
primoper  -x,y,z
centoper  x,y,z
endofdef


spgid  27
sspgname  P c c 2 
fspgname  P c c 2
pgname    m m 2 
crysym    orthorhombic 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  x,-y,z+1/2
primoper  -x,y,z+1/2
centoper  x,y,z
endofdef


spgid  28
sspgname  P m a 2 
fspgname  P m a 2
pgname    m m 2 
crysym    orthorhombic 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<1
primoper  x,y,z
primoper  -x,-y,z
primoper  x+1/2,-y,z
primoper  -x+1/2,y,z
centoper  x,y,z
endofdef


spgid  29
sspgname  P c a 21 
fspgname  P c a 21
pgname    m m 2 
crysym    orthorhombic 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z+1/2
primoper  x+1/2,-y,z
primoper  -x+1/2,y,z+1/2
centoper  x,y,z
endofdef


spgid  30
sspgname  P n c 2 
fspgname  P n c 2
pgname    m m 2 
crysym    orthorhombic 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  x,-y+1/2,z+1/2
primoper  -x,y+1/2,z+1/2
centoper  x,y,z
endofdef


spgid  31
sspgname  P m n 21 
fspgname  P m n 21
pgname    m m 2 
crysym    orthorhombic 
xyzasu    0<=x<=1/2; 0<=y<1; 0<=z<=1/2
primoper  x,y,z
primoper  -x+1/2,-y,z+1/2
primoper  x+1/2,-y,z+1/2
primoper  -x,y,z
centoper  x,y,z
endofdef


spgid  32
sspgname  P b a 2 
fspgname  P b a 2
pgname    m m 2 
crysym    orthorhombic 
xyzasu    0<=x<1; 0<=y<=1/4; 0<=z<1
primoper  x,y,z
primoper  -x,-y,z
primoper  x+1/2,-y+1/2,z
primoper  -x+1/2,y+1/2,z
centoper  x,y,z
endofdef


spgid  33
sspgname  P n a 21 
fspgname  P n a 21
pgname    m m 2 
crysym    orthorhombic 
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z+1/2
primoper  x+1/2,-y+1/2,z
primoper  -x+1/2,y+1/2,z+1/2
centoper  x,y,z
endofdef


spgid  34
sspgname  P n n 2 
fspgname  P n n 2
pgname    m m 2 
crysym    orthorhombic 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  x+1/2,-y+1/2,z+1/2
primoper  -x+1/2,y+1/2,z+1/2
centoper  x,y,z
endofdef


spgid  35
sspgname  C m m 2 
fspgname  C m m 2
pgname    m m 2 
crysym    orthorhombic 
xyzasu    0<=x<=1/2; 0<=y<=1/4; 0<=z<1
primoper  x,y,z
primoper  -x,-y,z
primoper  x,-y,z
primoper  -x,y,z
centoper  x,y,z
centoper  x+1/2,y+1/2,z
endofdef


spgid  36
sspgname  C m c 21 
fspgname  C m c 21
pgname    m m 2 
crysym    orthorhombic 
xyzasu    0<=x<=1/2; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z+1/2
primoper  x,-y,z+1/2
primoper  -x,y,z
centoper  x,y,z
centoper  x+1/2,y+1/2,z
endofdef


spgid  37
sspgname  C c c 2 
fspgname  C c c 2
pgname    m m 2 
crysym    orthorhombic 
xyzasu    0<=x<1; 0<=y<=1/4; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  x,-y,z+1/2
primoper  -x,y,z+1/2
centoper  x,y,z
centoper  x+1/2,y+1/2,z
endofdef


spgid  38
sspgname  A m m 2 
fspgname  A m m 2
pgname    m m 2 
crysym    orthorhombic 
xyzasu    0<=x<=1/2; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  x,-y,z
primoper  -x,y,z
centoper  x,y,z
centoper  x,y+1/2,z+1/2
endofdef


spgid  39
sspgname  A e m 2 
fspgname  A e m 2
pgname    m m 2 
crysym    orthorhombic 
xyzasu    0<=x<1; 0<=y<=1/4; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  x,-y+1/2,z
primoper  -x,y+1/2,z
centoper  x,y,z
centoper  x,y+1/2,z+1/2
endofdef


spgid  40
sspgname  A m a 2 
fspgname  A m a 2
pgname    m m 2 
crysym    orthorhombic 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  x+1/2,-y,z
primoper  -x+1/2,y,z
centoper  x,y,z
centoper  x,y+1/2,z+1/2
endofdef


spgid  41
sspgname  A e a 2 
fspgname  A b a 2
pgname    m m 2 
crysym    orthorhombic 
xyzasu    0<=x<1; 0<=y<=1/4; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  x+1/2,-y+1/2,z
primoper  -x+1/2,y+1/2,z
centoper  x,y,z
centoper  x,y+1/2,z+1/2
endofdef


spgid  42
sspgname  F m m 2 
fspgname  F m m 2
pgname    m m 2 
crysym    orthorhombic 
xyzasu    0<=x<=1/2; 0<=y<=1/4; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  x,-y,z
primoper  -x,y,z
centoper  x,y,z
centoper  x,y+1/2,z+1/2
centoper  x+1/2,y,z+1/2
centoper  x+1/2,y+1/2,z
endofdef


spgid  43
sspgname  F d d 2 
fspgname  F d d 2
pgname    m m 2 
crysym    orthorhombic 
xyzasu    0<=x<1; 0<=y<=1/4; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  x+1/4,-y+1/4,z+1/4
primoper  -x+1/4,y+1/4,z+1/4
centoper  x,y,z
centoper  x,y+1/2,z+1/2
centoper  x+1/2,y,z+1/2
centoper  x+1/2,y+1/2,z
endofdef


spgid  44
sspgname  I m m 2 
fspgname  I m m 2
pgname    m m 2 
crysym    orthorhombic 
xyzasu    0<=x<=1/2; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  x,-y,z
primoper  -x,y,z
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef


spgid  45
sspgname  I b a 2 
fspgname  I b a 2
pgname    m m 2 
crysym    orthorhombic 
xyzasu    0<=x<1; 0<=y<=1/4; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  x+1/2,-y+1/2,z
primoper  -x+1/2,y+1/2,z
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef


spgid  46
sspgname  I m a 2 
fspgname  I m a 2
pgname    m m 2 
crysym    orthorhombic 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  x+1/2,-y,z
primoper  -x+1/2,y,z
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef


spgid  47
sspgname  P m m m 
fspgname  P 2/m 2/m 2/m
pgname    m m m 
crysym    orthorhombic 
xyzasu    0<=x<=1/2; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  -x,y,-z
primoper  x,-y,-z
primoper  -x,-y,-z
primoper  x,y,-z
primoper  x,-y,z
primoper  -x,y,z
centoper  x,y,z
endofdef


spgid  48
sspgname  P n n n 
fspgname  P 2/n 2/n 2/n
pgname    m m m 
crysym    orthorhombic 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -x,y,-z
primoper  x,-y,-z
primoper  -x+1/2,-y+1/2,-z+1/2
primoper  x+1/2,y+1/2,-z+1/2
primoper  x+1/2,-y+1/2,z+1/2
primoper  -x+1/2,y+1/2,z+1/2
centoper  x,y,z
endofdef


spgid  49
sspgname  P c c m 
fspgname  P 2/c 2/c 2/m
pgname    m m m 
crysym    orthorhombic 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -x,y,-z+1/2
primoper  x,-y,-z+1/2
primoper  -x,-y,-z
primoper  x,y,-z
primoper  x,-y,z+1/2
primoper  -x,y,z+1/2
centoper  x,y,z
endofdef


spgid  50
sspgname  P b a n 
fspgname  P 2/b 2/a 2/n
pgname    m m m 
crysym    orthorhombic 
xyzasu    0<=x<1; 0<=y<=1/4; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  -x,y,-z
primoper  x,-y,-z
primoper  -x+1/2,-y+1/2,-z
primoper  x+1/2,y+1/2,-z
primoper  x+1/2,-y+1/2,z
primoper  -x+1/2,y+1/2,z
centoper  x,y,z
endofdef


spgid  51
sspgname  P m m a 
fspgname  P 21/m 2/m 2/a
pgname    m m m 
crysym    orthorhombic 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x+1/2,-y,z
primoper  -x,y,-z
primoper  x+1/2,-y,-z
primoper  -x,-y,-z
primoper  x+1/2,y,-z
primoper  x,-y,z
primoper  -x+1/2,y,z
centoper  x,y,z
endofdef


spgid  52
sspgname  P n n a 
fspgname  P 2/n 21/n 2/a
pgname    m m m 
crysym    orthorhombic 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x+1/2,-y,z
primoper  -x+1/2,y+1/2,-z+1/2
primoper  x,-y+1/2,-z+1/2
primoper  -x,-y,-z
primoper  x+1/2,y,-z
primoper  x+1/2,-y+1/2,z+1/2
primoper  -x,y+1/2,z+1/2
centoper  x,y,z
endofdef


spgid  53
sspgname  P m n a 
fspgname  P 2/m 2/n 21/a
pgname    m m m 
crysym    orthorhombic 
xyzasu    0<=x<=1/2; 0<=y<1; 0<=z<=1/4
primoper  x,y,z
primoper  -x+1/2,-y,z+1/2
primoper  -x+1/2,y,-z+1/2
primoper  x,-y,-z
primoper  -x,-y,-z
primoper  x+1/2,y,-z+1/2
primoper  x+1/2,-y,z+1/2
primoper  -x,y,z
centoper  x,y,z
endofdef


spgid  54
sspgname  P c c a 
fspgname  P 21/c 2/c 2/a
pgname    m m m 
crysym    orthorhombic 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x+1/2,-y,z
primoper  -x,y,-z+1/2
primoper  x+1/2,-y,-z+1/2
primoper  -x,-y,-z
primoper  x+1/2,y,-z
primoper  x,-y,z+1/2
primoper  -x+1/2,y,z+1/2
centoper  x,y,z
endofdef


spgid  55
sspgname  P b a m 
fspgname  P 21/b 21/a 2/m
pgname    m m m 
crysym    orthorhombic 
xyzasu    0<=x<1; 0<=y<=1/4; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  -x+1/2,y+1/2,-z
primoper  x+1/2,-y+1/2,-z
primoper  -x,-y,-z
primoper  x,y,-z
primoper  x+1/2,-y+1/2,z
primoper  -x+1/2,y+1/2,z
centoper  x,y,z
endofdef


spgid  56
sspgname  P c c n 
fspgname  P 21/c 21/c 2/n
pgname    m m m 
crysym    orthorhombic 
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/4
primoper  x,y,z
primoper  -x+1/2,-y+1/2,z
primoper  -x,y+1/2,-z+1/2
primoper  x+1/2,-y,-z+1/2
primoper  -x,-y,-z
primoper  x+1/2,y+1/2,-z
primoper  x,-y+1/2,z+1/2
primoper  -x+1/2,y,z+1/2
centoper  x,y,z
endofdef


spgid  57
sspgname  P b c m 
fspgname  P 2/b 21/c 21/m
pgname    m m m 
crysym    orthorhombic 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z+1/2
primoper  -x,y+1/2,-z+1/2
primoper  x,-y+1/2,-z
primoper  -x,-y,-z
primoper  x,y,-z+1/2
primoper  x,-y+1/2,z+1/2
primoper  -x,y+1/2,z
centoper  x,y,z
endofdef


spgid  58
sspgname  P n n m 
fspgname  P 21/n 21/n 2/m
pgname    m m m 
crysym    orthorhombic 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -x+1/2,y+1/2,-z+1/2
primoper  x+1/2,-y+1/2,-z+1/2
primoper  -x,-y,-z
primoper  x,y,-z
primoper  x+1/2,-y+1/2,z+1/2
primoper  -x+1/2,y+1/2,z+1/2
centoper  x,y,z
endofdef


spgid  59
sspgname  P m m n 
fspgname  P 21/m 21/m 2/n
pgname    m m m 
crysym    orthorhombic 
xyzasu    0<=x<=1/2; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  -x+1/2,y+1/2,-z
primoper  x+1/2,-y+1/2,-z
primoper  -x+1/2,-y+1/2,-z
primoper  x+1/2,y+1/2,-z
primoper  x,-y,z
primoper  -x,y,z
centoper  x,y,z
endofdef


spgid  60
sspgname  P b c n 
fspgname  P 21/b 2/c 21/n
pgname    m m m 
crysym    orthorhombic 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x+1/2,-y+1/2,z+1/2
primoper  -x,y,-z+1/2
primoper  x+1/2,-y+1/2,-z
primoper  -x,-y,-z
primoper  x+1/2,y+1/2,-z+1/2
primoper  x,-y,z+1/2
primoper  -x+1/2,y+1/2,z
centoper  x,y,z
endofdef


spgid  61
sspgname  P b c a 
fspgname  P 21/b 21/c 21/a
pgname    m m m 
crysym    orthorhombic 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x+1/2,-y,z+1/2
primoper  -x,y+1/2,-z+1/2
primoper  x+1/2,-y+1/2,-z
primoper  -x,-y,-z
primoper  x+1/2,y,-z+1/2
primoper  x,-y+1/2,z+1/2
primoper  -x+1/2,y+1/2,z
centoper  x,y,z
endofdef


spgid  62
sspgname  P n m a 
fspgname  P 21/n 21/m 21/a
pgname    m m m 
crysym    orthorhombic 
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/4
primoper  x,y,z
primoper  -x+1/2,-y,z+1/2
primoper  -x,y+1/2,-z
primoper  x+1/2,-y+1/2,-z+1/2
primoper  -x,-y,-z
primoper  x+1/2,y,-z+1/2
primoper  x,-y+1/2,z
primoper  -x+1/2,y+1/2,z+1/2
centoper  x,y,z
endofdef


spgid  63
sspgname  C m c m 
fspgname  C 2/m 2/c 21/m
pgname    m m m 
crysym    orthorhombic 
xyzasu    0<=x<=1/2; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z+1/2
primoper  -x,y,-z+1/2
primoper  x,-y,-z
primoper  -x,-y,-z
primoper  x,y,-z+1/2
primoper  x,-y,z+1/2
primoper  -x,y,z
centoper  x,y,z
centoper  x+1/2,y+1/2,z
endofdef


spgid  64
sspgname  C m c e 
fspgname  C 2/m 2/c 21/e
pgname    m m m 
crysym    orthorhombic 
xyzasu    0<=x<=1/2; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y+1/2,z+1/2
primoper  -x,y+1/2,-z+1/2
primoper  x,-y,-z
primoper  -x,-y,-z
primoper  x,y+1/2,-z+1/2
primoper  x,-y+1/2,z+1/2
primoper  -x,y,z
centoper  x,y,z
centoper  x+1/2,y+1/2,z
endofdef


spgid  65
sspgname  C m m m 
fspgname  C 2/m 2/m 2/m
pgname    m m m 
crysym    orthorhombic 
xyzasu    0<=x<=1/2; 0<=y<=1/4; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  -x,y,-z
primoper  x,-y,-z
primoper  -x,-y,-z
primoper  x,y,-z
primoper  x,-y,z
primoper  -x,y,z
centoper  x,y,z
centoper  x+1/2,y+1/2,z
endofdef


spgid  66
sspgname  C c c m 
fspgname  C 2/c 2/c 2/m
pgname    m m m 
crysym    orthorhombic 
xyzasu    0<=x<1; 0<=y<=1/4; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -x,y,-z+1/2
primoper  x,-y,-z+1/2
primoper  -x,-y,-z
primoper  x,y,-z
primoper  x,-y,z+1/2
primoper  -x,y,z+1/2
centoper  x,y,z
centoper  x+1/2,y+1/2,z
endofdef


spgid  67
sspgname  C m m e 
fspgname  C 2/m 2/m 2/e
pgname    m m m 
crysym    orthorhombic 
xyzasu    0<=x<=1/2; 0<=y<=1/4; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y+1/2,z
primoper  -x,y+1/2,-z
primoper  x,-y,-z
primoper  -x,-y,-z
primoper  x,y+1/2,-z
primoper  x,-y+1/2,z
primoper  -x,y,z
centoper  x,y,z
centoper  x+1/2,y+1/2,z
endofdef


spgid  68
sspgname  C c c e 
fspgname  C 2/c 2/c 2/e
pgname    m m m 
crysym    orthorhombic 
xyzasu    0<=x<1; 0<=y<=1/4; 0<=z<=1/4
primoper  x,y,z
primoper  -x+1/2,-y+1/2,z
primoper  -x,y,-z
primoper  x+1/2,-y+1/2,-z
primoper  -x,-y+1/2,-z+1/2
primoper  x+1/2,y,-z+1/2
primoper  x,-y+1/2,z+1/2
primoper  -x+1/2,y,z+1/2
centoper  x,y,z
centoper  x+1/2,y+1/2,z
endofdef


spgid  69
sspgname  F m m m 
fspgname  F 2/m 2/m 2/m
pgname    m m m 
crysym    orthorhombic 
xyzasu    0<=x<=1/2; 0<=y<=1/4; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -x,y,-z
primoper  x,-y,-z
primoper  -x,-y,-z
primoper  x,y,-z
primoper  x,-y,z
primoper  -x,y,z
centoper  x,y,z
centoper  x,y+1/2,z+1/2
centoper  x+1/2,y,z+1/2
centoper  x+1/2,y+1/2,z
endofdef


spgid  70
sspgname  F d d d 
fspgname  F 2/d 2/d 2/d
pgname    m m m 
crysym    orthorhombic 
xyzasu    0<=x<1; 0<=y<=1/4; 0<=z<=1/8
primoper  x,y,z
primoper  -x,-y,z
primoper  -x,y,-z
primoper  x,-y,-z
primoper  -x+1/4,-y+1/4,-z+1/4
primoper  x+1/4,y+1/4,-z+1/4
primoper  x+1/4,-y+1/4,z+1/4
primoper  -x+1/4,y+1/4,z+1/4
centoper  x,y,z
centoper  x,y+1/2,z+1/2
centoper  x+1/2,y,z+1/2
centoper  x+1/2,y+1/2,z
endofdef


spgid  71
sspgname  I m m m 
fspgname  I 2/m 2/m 2/m
pgname    m m m 
crysym    orthorhombic 
xyzasu    0<=x<=1/2; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -x,y,-z
primoper  x,-y,-z
primoper  -x,-y,-z
primoper  x,y,-z
primoper  x,-y,z
primoper  -x,y,z
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef


spgid  72
sspgname  I b a m 
fspgname  I 2/b 2/a 2/m
pgname    m m m 
crysym    orthorhombic 
xyzasu    0<=x<1; 0<=y<=1/4; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -x+1/2,y+1/2,-z
primoper  x+1/2,-y+1/2,-z
primoper  -x,-y,-z
primoper  x,y,-z
primoper  x+1/2,-y+1/2,z
primoper  -x+1/2,y+1/2,z
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef


spgid  73
sspgname  I b c a 
fspgname  I 21/b 21/c 21/a
pgname    m m m 
crysym    orthorhombic 
xyzasu    0<=x<1; 0<=y<=1/4; 0<=z<=1/4
primoper  x,y,z
primoper  -x+1/2,-y,z+1/2
primoper  -x,y+1/2,-z+1/2
primoper  x+1/2,-y+1/2,-z
primoper  -x,-y,-z
primoper  x+1/2,y,-z+1/2
primoper  x,-y+1/2,z+1/2
primoper  -x+1/2,y+1/2,z
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef


spgid  74
sspgname  I m m a 
fspgname  I 21/m 21/m 21/a
pgname    m m m 
crysym    orthorhombic 
xyzasu    0<=x<=1/2; 0<=y<1; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y+1/2,z
primoper  -x,y+1/2,-z
primoper  x,-y,-z
primoper  -x,-y,-z
primoper  x,y+1/2,-z
primoper  x,-y+1/2,z
primoper  -x,y,z
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef


spgid  75
sspgname  P 4 
fspgname  P 4
pgname    4 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<1
primoper  x,y,z
primoper  -x,-y,z
primoper  -y,x,z
primoper  y,-x,z
centoper  x,y,z
endofdef


spgid  76
sspgname  P 41 
fspgname  P 41
pgname    4 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z+1/2
primoper  -y,x,z+1/4
primoper  y,-x,z+3/4
centoper  x,y,z
endofdef


spgid  77
sspgname  P 42 
fspgname  P 42
pgname    4 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  -y,x,z+1/2
primoper  y,-x,z+1/2
centoper  x,y,z
endofdef


spgid  78
sspgname  P 43 
fspgname  P 43
pgname    4 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z+1/2
primoper  -y,x,z+3/4
primoper  y,-x,z+1/4
centoper  x,y,z
endofdef


spgid  79
sspgname  I 4 
fspgname  I 4
pgname    4 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  -y,x,z
primoper  y,-x,z
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef


spgid  80
sspgname  I 41 
fspgname  I 41
pgname    4 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x+1/2,-y+1/2,z+1/2
primoper  -y,x+1/2,z+1/4
primoper  y+1/2,-x,z+3/4
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef


spgid  81
sspgname  P -4 
fspgname  P -4
pgname    -4 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  y,-x,-z
primoper  -y,x,-z
centoper  x,y,z
endofdef


spgid  82
sspgname  I -4 
fspgname  I -4
pgname    -4 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  y,-x,-z
primoper  -y,x,-z
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef


spgid  83
sspgname  P 4/m 
fspgname  P 4/m
pgname    4/m 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  -y,x,z
primoper  y,-x,z
primoper  -x,-y,-z
primoper  x,y,-z
primoper  y,-x,-z
primoper  -y,x,-z
centoper  x,y,z
endofdef


spgid  84
sspgname  P 42/m 
fspgname  P 42/m
pgname    4/m 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -y,x,z+1/2
primoper  y,-x,z+1/2
primoper  -x,-y,-z
primoper  x,y,-z
primoper  y,-x,-z+1/2
primoper  -y,x,-z+1/2
centoper  x,y,z
endofdef


spgid  85
sspgname  P 4/n 
fspgname  P 4/n
pgname    4/m 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  -y+1/2,x+1/2,z
primoper  y+1/2,-x+1/2,z
primoper  -x+1/2,-y+1/2,-z
primoper  x+1/2,y+1/2,-z
primoper  y,-x,-z
primoper  -y,x,-z
centoper  x,y,z
endofdef


spgid  86
sspgname  P 42/n 
fspgname  P 42/n
pgname    4/m 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -y+1/2,x+1/2,z+1/2
primoper  y+1/2,-x+1/2,z+1/2
primoper  -x+1/2,-y+1/2,-z+1/2
primoper  x+1/2,y+1/2,-z+1/2
primoper  y,-x,-z
primoper  -y,x,-z
centoper  x,y,z
endofdef


spgid  87
sspgname  I 4/m 
fspgname  I 4/m
pgname    4/m 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -y,x,z
primoper  y,-x,z
primoper  -x,-y,-z
primoper  x,y,-z
primoper  y,-x,-z
primoper  -y,x,-z
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef


spgid  88
sspgname  I 41/a 
fspgname  I 41/a
pgname    4/m 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/8
primoper  x,y,z
primoper  -x+1/2,-y+1/2,z+1/2
primoper  -y,x+1/2,z+1/4
primoper  y+1/2,-x,z+3/4
primoper  -x,-y+1/2,-z+1/4
primoper  x+1/2,y,-z+3/4
primoper  y,-x,-z
primoper  -y+1/2,x+1/2,-z+1/2
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef


spgid  89
sspgname  P 4 2 2 
fspgname  P 4 2 2
pgname    4 2 2 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  -y,x,z
primoper  y,-x,z
primoper  -x,y,-z
primoper  x,-y,-z
primoper  y,x,-z
primoper  -y,-x,-z
centoper  x,y,z
endofdef


spgid  90
sspgname  P 4 21 2 
fspgname  P 4 21 2
pgname    422 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  -y+1/2,x+1/2,z
primoper  y+1/2,-x+1/2,z
primoper  -x+1/2,y+1/2,-z
primoper  x+1/2,-y+1/2,-z
primoper  y,x,-z
primoper  -y,-x,-z
centoper  x,y,z
endofdef


spgid  91
sspgname  P 41 2 2 
fspgname  P 41 2 2
pgname    4 2 2 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/8
primoper  x,y,z
primoper  -x,-y,z+1/2
primoper  -y,x,z+1/4
primoper  y,-x,z+3/4
primoper  -x,y,-z
primoper  x,-y,-z+1/2
primoper  y,x,-z+3/4
primoper  -y,-x,-z+1/4
centoper  x,y,z
endofdef


spgid  92
sspgname  P 41 21 2 
fspgname  P 41 21 2
pgname    4 2 2 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/8
primoper  x,y,z
primoper  -x,-y,z+1/2
primoper  -y+1/2,x+1/2,z+1/4
primoper  y+1/2,-x+1/2,z+3/4
primoper  -x+1/2,y+1/2,-z+1/4
primoper  x+1/2,-y+1/2,-z+3/4
primoper  y,x,-z
primoper  -y,-x,-z+1/2
centoper  x,y,z
endofdef


spgid  93
sspgname  P 42 2 2 
fspgname  P 42 2 2
pgname    4 2 2 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -y,x,z+1/2
primoper  y,-x,z+1/2
primoper  -x,y,-z
primoper  x,-y,-z
primoper  y,x,-z+1/2
primoper  -y,-x,-z+1/2
centoper  x,y,z
endofdef


spgid  94
sspgname  P 42 21 2 
fspgname  P 42 21 2
pgname    4 2 2 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -y+1/2,x+1/2,z+1/2
primoper  y+1/2,-x+1/2,z+1/2
primoper  -x+1/2,y+1/2,-z+1/2
primoper  x+1/2,-y+1/2,-z+1/2
primoper  y,x,-z
primoper  -y,-x,-z
centoper  x,y,z
endofdef


spgid  95
sspgname  P 43 2 2 
fspgname  P 43 2 2
pgname    4 2 2 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/8
primoper  x,y,z
primoper  -x,-y,z+1/2
primoper  -y,x,z+3/4
primoper  y,-x,z+1/4
primoper  -x,y,-z
primoper  x,-y,-z+1/2
primoper  y,x,-z+1/4
primoper  -y,-x,-z+3/4
centoper  x,y,z
endofdef


spgid  96
sspgname  P 43 21 2 
fspgname  P 43 21 2
pgname    4 2 2 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/8
primoper  x,y,z
primoper  -x,-y,z+1/2
primoper  -y+1/2,x+1/2,z+3/4
primoper  y+1/2,-x+1/2,z+1/4
primoper  -x+1/2,y+1/2,-z+3/4
primoper  x+1/2,-y+1/2,-z+1/4
primoper  y,x,-z
primoper  -y,-x,-z+1/2
centoper  x,y,z
endofdef


spgid  97
sspgname  I 4 2 2 
fspgname  I 4 2 2
pgname    4 2 2 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -y,x,z
primoper  y,-x,z
primoper  -x,y,-z
primoper  x,-y,-z
primoper  y,x,-z
primoper  -y,-x,-z
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef


spgid  98
sspgname  I 41 2 2 
fspgname  I 41 2 2
pgname    4 2 2 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/8
primoper  x,y,z
primoper  -x+1/2,-y+1/2,z+1/2
primoper  -y,x+1/2,z+1/4
primoper  y+1/2,-x,z+3/4
primoper  -x+1/2,y,-z+3/4
primoper  x,-y+1/2,-z+1/4
primoper  y+1/2,x+1/2,-z+1/2
primoper  -y,-x,-z
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef


spgid  99
sspgname  P 4 m m 
fspgname  P 4 m m
pgname    4 m m 
crysym    Tetragonal 
xyzasu    0<=x<=1/2; 0<=y<=1/2; 0<=z<1
primoper  x,y,z
primoper  -x,-y,z
primoper  -y,x,z
primoper  y,-x,z
primoper  x,-y,z
primoper  -x,y,z
primoper  -y,-x,z
primoper  y,x,z
centoper  x,y,z
endofdef


spgid  100
sspgname  P 4 b m 
fspgname  P 4 b m
pgname    4 m m 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/4; 0<=z<1
primoper  x,y,z
primoper  -x,-y,z
primoper  -y,x,z
primoper  y,-x,z
primoper  x+1/2,-y+1/2,z
primoper  -x+1/2,y+1/2,z
primoper  -y+1/2,-x+1/2,z
primoper  y+1/2,x+1/2,z
centoper  x,y,z
endofdef


spgid  101
sspgname  P 42 c m 
fspgname  P 42 c m
pgname    4 m m 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  -y,x,z+1/2
primoper  y,-x,z+1/2
primoper  x,-y,z+1/2
primoper  -x,y,z+1/2
primoper  -y,-x,z
primoper  y,x,z
centoper  x,y,z
endofdef


spgid  102
sspgname  P 42 n m 
fspgname  P 42 n m
pgname    4 m m 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  -y+1/2,x+1/2,z+1/2
primoper  y+1/2,-x+1/2,z+1/2
primoper  x+1/2,-y+1/2,z+1/2
primoper  -x+1/2,y+1/2,z+1/2
primoper  -y,-x,z
primoper  y,x,z
centoper  x,y,z
endofdef


spgid  103
sspgname  P 4 c c 
fspgname  P 4 c c
pgname    4 m m 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  -y,x,z
primoper  y,-x,z
primoper  x,-y,z+1/2
primoper  -x,y,z+1/2
primoper  -y,-x,z+1/2
primoper  y,x,z+1/2
centoper  x,y,z
endofdef


spgid  104
sspgname  P 4 n c 
fspgname  P 4 n c
pgname    4 m m 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  -y,x,z
primoper  y,-x,z
primoper  x+1/2,-y+1/2,z+1/2
primoper  -x+1/2,y+1/2,z+1/2
primoper  -y+1/2,-x+1/2,z+1/2
primoper  y+1/2,x+1/2,z+1/2
centoper  x,y,z
endofdef


spgid  105
sspgname  P 42 m c 
fspgname  P 42 m c
pgname    4 m m 
crysym    Tetragonal 
xyzasu    0<=x<=1/2; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  -y,x,z+1/2
primoper  y,-x,z+1/2
primoper  x,-y,z
primoper  -x,y,z
primoper  -y,-x,z+1/2
primoper  y,x,z+1/2
centoper  x,y,z
endofdef


spgid  106
sspgname  P 42 b c 
fspgname  P 42 b c
pgname    4 m m 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/4; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  -y,x,z+1/2
primoper  y,-x,z+1/2
primoper  x+1/2,-y+1/2,z
primoper  -x+1/2,y+1/2,z
primoper  -y+1/2,-x+1/2,z+1/2
primoper  y+1/2,x+1/2,z+1/2
centoper  x,y,z
endofdef


spgid  107
sspgname  I 4 m m 
fspgname  I 4 m m
pgname    4 m m 
crysym    Tetragonal 
xyzasu    0<=x<=1/2; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  -y,x,z
primoper  y,-x,z
primoper  x,-y,z
primoper  -x,y,z
primoper  -y,-x,z
primoper  y,x,z
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef


spgid  108
sspgname  I 4 c m 
fspgname  I 4 c m
pgname    4 m m 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/4; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  -y,x,z
primoper  y,-x,z
primoper  x,-y,z+1/2
primoper  -x,y,z+1/2
primoper  -y,-x,z+1/2
primoper  y,x,z+1/2
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef


spgid  109
sspgname  I 41 m d 
fspgname  I 41 m d
pgname    4 m m 
crysym    Tetragonal 
xyzasu    0<=x<=1/2; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x+1/2,-y+1/2,z+1/2
primoper  -y,x+1/2,z+1/4
primoper  y+1/2,-x,z+3/4
primoper  x,-y,z
primoper  -x+1/2,y+1/2,z+1/2
primoper  -y,-x+1/2,z+1/4
primoper  y+1/2,x,z+3/4
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef


spgid  110
sspgname  I 41 c d 
fspgname  I 41 c d
pgname    4 m m 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/4; 0<=z<=1/4
primoper  x,y,z
primoper  -x+1/2,-y+1/2,z+1/2
primoper  -y,x+1/2,z+1/4
primoper  y+1/2,-x,z+3/4
primoper  x,-y,z+1/2
primoper  -x+1/2,y+1/2,z
primoper  -y,-x+1/2,z+3/4
primoper  y+1/2,x,z+1/4
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef


spgid  111
sspgname  P -4 2 m 
fspgname  P -4 2 m
pgname    -4 2 m 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  y,-x,-z
primoper  -y,x,-z
primoper  -x,y,-z
primoper  x,-y,-z
primoper  -y,-x,z
primoper  y,x,z
centoper  x,y,z
endofdef


spgid  112
sspgname  P -4 2 c 
fspgname  P -4 2 c
pgname    -4 2 m 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  y,-x,-z
primoper  -y,x,-z
primoper  -x,y,-z+1/2
primoper  x,-y,-z+1/2
primoper  -y,-x,z+1/2
primoper  y,x,z+1/2
centoper  x,y,z
endofdef


spgid  113
sspgname  P -4 21 m 
fspgname  P -4 21 m
pgname    -4 2 m 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  y,-x,-z
primoper  -y,x,-z
primoper  -x+1/2,y+1/2,-z
primoper  x+1/2,-y+1/2,-z
primoper  -y+1/2,-x+1/2,z
primoper  y+1/2,x+1/2,z
centoper  x,y,z
endofdef


spgid  114
sspgname  P -4 21 c 
fspgname  P -4 21 c
pgname    -4 2 m 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  y,-x,-z
primoper  -y,x,-z
primoper  -x+1/2,y+1/2,-z+1/2
primoper  x+1/2,-y+1/2,-z+1/2
primoper  -y+1/2,-x+1/2,z+1/2
primoper  y+1/2,x+1/2,z+1/2
centoper  x,y,z
endofdef


spgid  115
sspgname  P -4 m 2 
fspgname  P -4 m 2
pgname    -4 m 2 
crysym    Tetragonal 
xyzasu    0<=x<=1/2; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  y,-x,-z
primoper  -y,x,-z
primoper  x,-y,z
primoper  -x,y,z
primoper  y,x,-z
primoper  -y,-x,-z
centoper  x,y,z
endofdef


spgid  116
sspgname  P -4 c 2 
fspgname  P -4 c 2
pgname    -4 m 2 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  y,-x,-z
primoper  -y,x,-z
primoper  x,-y,z+1/2
primoper  -x,y,z+1/2
primoper  y,x,-z+1/2
primoper  -y,-x,-z+1/2
centoper  x,y,z
endofdef


spgid  117
sspgname  P -4 b 2 
fspgname  P -4 b 2
pgname    -4 m 2 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/4; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  y,-x,-z
primoper  -y,x,-z
primoper  x+1/2,-y+1/2,z
primoper  -x+1/2,y+1/2,z
primoper  y+1/2,x+1/2,-z
primoper  -y+1/2,-x+1/2,-z
centoper  x,y,z
endofdef


spgid  118
sspgname  P -4 n 2 
fspgname  P -4 n 2
pgname    -4 m 2 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  y,-x,-z
primoper  -y,x,-z
primoper  x+1/2,-y+1/2,z+1/2
primoper  -x+1/2,y+1/2,z+1/2
primoper  y+1/2,x+1/2,-z+1/2
primoper  -y+1/2,-x+1/2,-z+1/2
centoper  x,y,z
endofdef


spgid  119
sspgname  I -4 m 2 
fspgname  I -4 m 2
pgname    -4 m 2 
crysym    Tetragonal 
xyzasu    0<=x<=1/2; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  y,-x,-z
primoper  -y,x,-z
primoper  x,-y,z
primoper  -x,y,z
primoper  y,x,-z
primoper  -y,-x,-z
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef


spgid  120
sspgname  I -4 c 2 
fspgname  I -4 c 2
pgname    -4 m 2 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/4; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  y,-x,-z
primoper  -y,x,-z
primoper  x,-y,z+1/2
primoper  -x,y,z+1/2
primoper  y,x,-z+1/2
primoper  -y,-x,-z+1/2
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef


spgid  121
sspgname  I -4 2 m 
fspgname  I -4 2 m
pgname    -4 2 m 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  y,-x,-z
primoper  -y,x,-z
primoper  -x,y,-z
primoper  x,-y,-z
primoper  -y,-x,z
primoper  y,x,z
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef


spgid  122
sspgname  I -4 2 d 
fspgname  I -4 2 d
pgname    -4 2 m 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/8
primoper  x,y,z
primoper  -x,-y,z
primoper  y,-x,-z
primoper  -y,x,-z
primoper  -x+1/2,y,-z+3/4
primoper  x+1/2,-y,-z+3/4
primoper  -y+1/2,-x,z+3/4
primoper  y+1/2,x,z+3/4
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef


spgid  123
sspgname  P 4/m m m 
fspgname  P 4/m 2/m 2/m
pgname    4/m m m 
crysym    Tetragonal 
xyzasu    0<=x<=1/2; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  -y,x,z
primoper  y,-x,z
primoper  -x,y,-z
primoper  x,-y,-z
primoper  y,x,-z
primoper  -y,-x,-z
primoper  -x,-y,-z
primoper  x,y,-z
primoper  y,-x,-z
primoper  -y,x,-z
primoper  x,-y,z
primoper  -x,y,z
primoper  -y,-x,z
primoper  y,x,z
centoper  x,y,z
endofdef


spgid  124
sspgname  P 4/m c c 
fspgname  P 4/m 2/c 2/c
pgname    4/m m m 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -y,x,z
primoper  y,-x,z
primoper  -x,y,-z+1/2
primoper  x,-y,-z+1/2
primoper  y,x,-z+1/2
primoper  -y,-x,-z+1/2
primoper  -x,-y,-z
primoper  x,y,-z
primoper  y,-x,-z
primoper  -y,x,-z
primoper  x,-y,z+1/2
primoper  -x,y,z+1/2
primoper  -y,-x,z+1/2
primoper  y,x,z+1/2
centoper  x,y,z
endofdef


spgid  125
sspgname  P 4/n b m 
fspgname  P 4/n 2/b 2/m
pgname    4/m m m 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/4; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  -y,x,z
primoper  y,-x,z
primoper  -x,y,-z
primoper  x,-y,-z
primoper  y,x,-z
primoper  -y,-x,-z
primoper  -x+1/2,-y+1/2,-z
primoper  x+1/2,y+1/2,-z
primoper  y+1/2,-x+1/2,-z
primoper  -y+1/2,x+1/2,-z
primoper  x+1/2,-y+1/2,z
primoper  -x+1/2,y+1/2,z
primoper  -y+1/2,-x+1/2,z
primoper  y+1/2,x+1/2,z
centoper  x,y,z
endofdef


spgid  126
sspgname  P 4/n n c 
fspgname  P 4/n 2/n 2/c 
pgname    4/m m m 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -y,x,z
primoper  y,-x,z
primoper  -x,y,-z
primoper  x,-y,-z
primoper  y,x,-z
primoper  -y,-x,-z
primoper  -x+1/2,-y+1/2,-z+1/2
primoper  x+1/2,y+1/2,-z+1/2
primoper  y+1/2,-x+1/2,-z+1/2
primoper  -y+1/2,x+1/2,-z+1/2
primoper  x+1/2,-y+1/2,z+1/2
primoper  -x+1/2,y+1/2,z+1/2
primoper  -y+1/2,-x+1/2,z+1/2
primoper  y+1/2,x+1/2,z+1/2
centoper  x,y,z
endofdef


spgid  127
sspgname  P 4/m b m 
fspgname  P 4/m 21/b 2/m
pgname    4/m m m 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/4; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  -y,x,z
primoper  y,-x,z
primoper  -x+1/2,y+1/2,-z
primoper  x+1/2,-y+1/2,-z
primoper  y+1/2,x+1/2,-z
primoper  -y+1/2,-x+1/2,-z
primoper  -x,-y,-z
primoper  x,y,-z
primoper  y,-x,-z
primoper  -y,x,-z
primoper  x+1/2,-y+1/2,z
primoper  -x+1/2,y+1/2,z
primoper  -y+1/2,-x+1/2,z
primoper  y+1/2,x+1/2,z
centoper  x,y,z
endofdef


spgid  128
sspgname  P 4/m n c 
fspgname  P 4/m 21/n 2/c
pgname    4/m m m 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -y,x,z
primoper  y,-x,z
primoper  -x+1/2,y+1/2,-z+1/2
primoper  x+1/2,-y+1/2,-z+1/2
primoper  y+1/2,x+1/2,-z+1/2
primoper  -y+1/2,-x+1/2,-z+1/2
primoper  -x,-y,-z
primoper  x,y,-z
primoper  y,-x,-z
primoper  -y,x,-z
primoper  x+1/2,-y+1/2,z+1/2
primoper  -x+1/2,y+1/2,z+1/2
primoper  -y+1/2,-x+1/2,z+1/2
primoper  y+1/2,x+1/2,z+1/2
centoper  x,y,z
endofdef


spgid  129
sspgname  P 4/n m m 
fspgname  P 4/n 21/m 2/m
pgname    4/m m m 
crysym    Tetragonal 
xyzasu    0<=x<=1/2; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  -y+1/2,x+1/2,z
primoper  y+1/2,-x+1/2,z
primoper  -x+1/2,y+1/2,-z
primoper  x+1/2,-y+1/2,-z
primoper  y,x,-z
primoper  -y,-x,-z
primoper  -x+1/2,-y+1/2,-z
primoper  x+1/2,y+1/2,-z
primoper  y,-x,-z
primoper  -y,x,-z
primoper  x,-y,z
primoper  -x,y,z
primoper  -y+1/2,-x+1/2,z
primoper  y+1/2,x+1/2,z
centoper  x,y,z
endofdef


spgid  130
sspgname  P 4/n c c 
fspgname  P 4/n 21/c 2/c
pgname    4/m m m 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -y+1/2,x+1/2,z
primoper  y+1/2,-x+1/2,z
primoper  -x+1/2,y+1/2,-z+1/2
primoper  x+1/2,-y+1/2,-z+1/2
primoper  y,x,-z+1/2
primoper  -y,-x,-z+1/2
primoper  -x+1/2,-y+1/2,-z
primoper  x+1/2,y+1/2,-z
primoper  y,-x,-z
primoper  -y,x,-z
primoper  x,-y,z+1/2
primoper  -x,y,z+1/2
primoper  -y+1/2,-x+1/2,z+1/2
primoper  y+1/2,x+1/2,z+1/2
centoper  x,y,z
endofdef


spgid  131
sspgname  P 42/m m c 
fspgname  P 42/m 2/m 2/c
pgname    4/m m m 
crysym    Tetragonal 
xyzasu    0<=x<=1/2; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -y,x,z+1/2
primoper  y,-x,z+1/2
primoper  -x,y,-z
primoper  x,-y,-z
primoper  y,x,-z+1/2
primoper  -y,-x,-z+1/2
primoper  -x,-y,-z
primoper  x,y,-z
primoper  y,-x,-z+1/2
primoper  -y,x,-z+1/2
primoper  x,-y,z
primoper  -x,y,z
primoper  -y,-x,z+1/2
primoper  y,x,z+1/2
centoper  x,y,z
endofdef


spgid  132
sspgname  P 42/m c m 
fspgname  P 42/m 2/c 2/m
pgname    4/m m m 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -y,x,z+1/2
primoper  y,-x,z+1/2
primoper  -x,y,-z+1/2
primoper  x,-y,-z+1/2
primoper  y,x,-z
primoper  -y,-x,-z
primoper  -x,-y,-z
primoper  x,y,-z
primoper  y,-x,-z+1/2
primoper  -y,x,-z+1/2
primoper  x,-y,z+1/2
primoper  -x,y,z+1/2
primoper  -y,-x,z
primoper  y,x,z
centoper  x,y,z
endofdef


spgid  133
sspgname  P 42/n b c 
fspgname  P 42/n 2/b 2/c
pgname    4/m m m 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/4; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -y+1/2,x+1/2,z+1/2
primoper  y+1/2,-x+1/2,z+1/2
primoper  -x,y,-z+1/2
primoper  x,-y,-z+1/2
primoper  y+1/2,x+1/2,-z
primoper  -y+1/2,-x+1/2,-z
primoper  -x+1/2,-y+1/2,-z+1/2
primoper  x+1/2,y+1/2,-z+1/2
primoper  y,-x,-z
primoper  -y,x,-z
primoper  x+1/2,-y+1/2,z
primoper  -x+1/2,y+1/2,z
primoper  -y,-x,z+1/2
primoper  y,x,z+1/2
centoper  x,y,z
endofdef


spgid  134
sspgname  P 42/n n m 
fspgname  P 42/n 2/n 2/m
pgname    4/m m m 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -y+1/2,x+1/2,z+1/2
primoper  y+1/2,-x+1/2,z+1/2
primoper  -x,y,-z
primoper  x,-y,-z
primoper  y+1/2,x+1/2,-z+1/2
primoper  -y+1/2,-x+1/2,-z+1/2
primoper  -x+1/2,-y+1/2,-z+1/2
primoper  x+1/2,y+1/2,-z+1/2
primoper  y,-x,-z
primoper  -y,x,-z
primoper  x+1/2,-y+1/2,z+1/2
primoper  -x+1/2,y+1/2,z+1/2
primoper  -y,-x,z
primoper  y,x,z
centoper  x,y,z
endofdef


spgid  135
sspgname  P 42/m b c 
fspgname  P 42/m 21/b 2/c
pgname    4/m m m 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/4; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -y,x,z+1/2
primoper  y,-x,z+1/2
primoper  -x+1/2,y+1/2,-z
primoper  x+1/2,-y+1/2,-z
primoper  y+1/2,x+1/2,-z+1/2
primoper  -y+1/2,-x+1/2,-z+1/2
primoper  -x,-y,-z
primoper  x,y,-z
primoper  y,-x,-z+1/2
primoper  -y,x,-z+1/2
primoper  x+1/2,-y+1/2,z
primoper  -x+1/2,y+1/2,z
primoper  -y+1/2,-x+1/2,z+1/2
primoper  y+1/2,x+1/2,z+1/2
centoper  x,y,z
endofdef


spgid  136
sspgname  P 42/m n m 
fspgname  P 42/m 21/n 2/m
pgname    4/m m m 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -y+1/2,x+1/2,z+1/2
primoper  y+1/2,-x+1/2,z+1/2
primoper  -x+1/2,y+1/2,-z+1/2
primoper  x+1/2,-y+1/2,-z+1/2
primoper  y,x,-z
primoper  -y,-x,-z
primoper  -x,-y,-z
primoper  x,y,-z
primoper  y+1/2,-x+1/2,-z+1/2
primoper  -y+1/2,x+1/2,-z+1/2
primoper  x+1/2,-y+1/2,z+1/2
primoper  -x+1/2,y+1/2,z+1/2
primoper  -y,-x,z
primoper  y,x,z
centoper  x,y,z
endofdef


spgid  137
sspgname  P 42/n m c 
fspgname  P 42/n 21/m 2/c
pgname    4/m m m 
crysym    Tetragonal 
xyzasu    0<=x<=1/2; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -y+1/2,x+1/2,z+1/2
primoper  y+1/2,-x+1/2,z+1/2
primoper  -x+1/2,y+1/2,-z+1/2
primoper  x+1/2,-y+1/2,-z+1/2
primoper  y,x,-z
primoper  -y,-x,-z
primoper  -x+1/2,-y+1/2,-z+1/2
primoper  x+1/2,y+1/2,-z+1/2
primoper  y,-x,-z
primoper  -y,x,-z
primoper  x,-y,z
primoper  -x,y,z
primoper  -y+1/2,-x+1/2,z+1/2
primoper  y+1/2,x+1/2,z+1/2
centoper  x,y,z
endofdef


spgid  138
sspgname  P 42/n c m 
fspgname  P 42/n 21/c 2/m
pgname    4/m m m 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -y+1/2,x+1/2,z+1/2
primoper  y+1/2,-x+1/2,z+1/2
primoper  -x+1/2,y+1/2,-z
primoper  x+1/2,-y+1/2,-z
primoper  y,x,-z+1/2
primoper  -y,-x,-z+1/2
primoper  -x+1/2,-y+1/2,-z+1/2
primoper  x+1/2,y+1/2,-z+1/2
primoper  y,-x,-z
primoper  -y,x,-z
primoper  x,-y,z+1/2
primoper  -x,y,z+1/2
primoper  -y+1/2,-x+1/2,z
primoper  y+1/2,x+1/2,z
centoper  x,y,z
endofdef


spgid  139
sspgname  I 4/m m m 
fspgname  I 4/m 2/m 2/m
pgname    4/m m m 
crysym    Tetragonal 
xyzasu    0<=x<=1/2; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -y,x,z
primoper  y,-x,z
primoper  -x,y,-z
primoper  x,-y,-z
primoper  y,x,-z
primoper  -y,-x,-z
primoper  -x,-y,-z
primoper  x,y,-z
primoper  y,-x,-z
primoper  -y,x,-z
primoper  x,-y,z
primoper  -x,y,z
primoper  -y,-x,z
primoper  y,x,z
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef


spgid  140
sspgname  I 4/m c m 
fspgname  I 4/m 2/c 2/m
pgname    4/m m m 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/4; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -y,x,z
primoper  y,-x,z
primoper  -x,y,-z+1/2
primoper  x,-y,-z+1/2
primoper  y,x,-z+1/2
primoper  -y,-x,-z+1/2
primoper  -x,-y,-z
primoper  x,y,-z
primoper  y,-x,-z
primoper  -y,x,-z
primoper  x,-y,z+1/2
primoper  -x,y,z+1/2
primoper  -y,-x,z+1/2
primoper  y,x,z+1/2
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef


spgid  141
sspgname  I 41/a m d 
fspgname  I 41/a 2/m 2/d
pgname    4/m m m 
crysym    Tetragonal
xyzasu    0<=x<=1/2; 0<=y<=1/2; 0<=z<=1/8 
primoper  x,y,z
primoper  -x+1/2,-y+1/2,z+1/2
primoper  -y,x+1/2,z+1/4
primoper  y+1/2,-x,z+3/4
primoper  -x+1/2,y,-z+3/4
primoper  x,-y+1/2,-z+1/4
primoper  y+1/2,x+1/2,-z+1/2
primoper  -y,-x,-z
primoper  -x,-y+1/2,-z+1/4
primoper  x+1/2,y,-z+3/4
primoper  y,-x,-z
primoper  -y+1/2,x+1/2,-z+1/2
primoper  x+1/2,-y+1/2,z+1/2
primoper  -x,y,z
primoper  -y+1/2,-x,z+3/4
primoper  y,x+1/2,z+1/4
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef


spgid  142
sspgname  I 41/a c d 
fspgname  I 41/a 2/c 2/d
pgname    4/m m m 
crysym    Tetragonal 
xyzasu    0<=x<1; 0<=y<=1/4; 0<=z<=1/8
primoper  x,y,z
primoper  -x+1/2,-y+1/2,z+1/2
primoper  -y,x+1/2,z+1/4
primoper  y+1/2,-x,z+3/4
primoper  -x+1/2,y,-z+1/4
primoper  x,-y+1/2,-z+3/4
primoper  y+1/2,x+1/2,-z
primoper  -y,-x,-z+1/2
primoper  -x,-y+1/2,-z+1/4
primoper  x+1/2,y,-z+3/4
primoper  y,-x,-z
primoper  -y+1/2,x+1/2,-z+1/2
primoper  x+1/2,-y+1/2,z
primoper  -x,y,z+1/2
primoper  -y+1/2,-x,z+1/4
primoper  y,x+1/2,z+3/4
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef


spgid  143
sspgname  P 3 
fspgname  P 3
pgname    3 
crysym    trigonal 
xyzasu    0<=x<1; 0<=y<=2/3; 0<=z<1
primoper  x,y,z
primoper  -y,x-y,z
primoper  -x+y,-x,z
centoper  x,y,z
endofdef


spgid  144
sspgname  P 31 
fspgname  P 31
pgname    3 
crysym    trigonal 
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/3
primoper  x,y,z
primoper  -y,x-y,z+1/3
primoper  -x+y,-x,z+2/3
centoper  x,y,z
endofdef


spgid  145
sspgname  P 32 
fspgname  P 32
pgname    3 
crysym    trigonal 
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/3
primoper  x,y,z
primoper  -y,x-y,z+2/3
primoper  -x+y,-x,z+1/3
centoper  x,y,z
endofdef

spgid  146
sspgname  R 3 
fspgname  R 3
pgname    3 
crysym    trigonal 
xyzasu    0<=x<1; 0<=y<=1; 0<=z<1
primoper  x,y,z
primoper  z,x,y
primoper  y,z,x
centoper  x,y,z
endofdef

spgid  146
sspgname  H 3 
fspgname  H 3
pgname    3 
crysym    trigonal 
xyzasu    0<=x<1; 0<=y<=2/3; 0<=z<=1/3
primoper  x,y,z
primoper  -y,x-y,z
primoper  -x+y,-x,z
centoper  x,y,z
centoper  x+2/3,y+1/3,z+1/3
centoper  x+1/3,y+2/3,z+2/3
endofdef

spgid  147
sspgname  P -3 
fspgname  P -3
pgname    -3 
crysym    trigonal 
xyzasu    0<=x<1; 0<=y<=2/3; 0<=z<=1/2
primoper  x,y,z
primoper  -y,x-y,z
primoper  -x+y,-x,z
primoper  -x,-y,-z
primoper  y,-x+y,-z
primoper  x-y,x,-z
centoper  x,y,z
endofdef

spgid  148
sspgname  R -3 
fspgname  R -3
pgname    -3 
crysym    trigonal 
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/2
primoper  x,y,z
primoper  z,x,y
primoper  y,z,x
primoper  -x,-y,-z
primoper  -z,-x,-y
primoper  -y,-z,-x
centoper  x,y,z
endofdef

spgid  148
sspgname  H -3 
fspgname  H -3
pgname    -3 
crysym    trigonal 
xyzasu    0<=x<1; 0<=y<=2/3; 0<=z<=1/6
primoper  x,y,z
primoper  -y,x-y,z
primoper  -x+y,-x,z
primoper  -x,-y,-z
primoper  y,-x+y,-z
primoper  x-y,x,-z
centoper  x,y,z
centoper  x+2/3,y+1/3,z+1/3
centoper  x+1/3,y+2/3,z+2/3
endofdef

spgid  149
sspgname  P 3 1 2 
fspgname  P 3 1 2
pgname    3 1 2 
crysym    trigonal 
xyzasu    0<=x<1; 0<=y<=2/3; 0<=z<=1/2
primoper  x,y,z
primoper  -y,x-y,z
primoper  -x+y,-x,z
primoper  -y,-x,-z
primoper  -x+y,y,-z
primoper  x,x-y,-z
centoper  x,y,z
endofdef


spgid  150
sspgname  P 3 2 1 
fspgname  P 3 2 1
pgname    3 2 1 
crysym    trigonal 
xyzasu    0<=x<1; 0<=y<=2/3; 0<=z<=1/2
primoper  x,y,z
primoper  -y,x-y,z
primoper  -x+y,-x,z
primoper  y,x,-z
primoper  x-y,-y,-z
primoper  -x,-x+y,-z
centoper  x,y,z
endofdef


spgid  151
sspgname  P 31 1 2 
fspgname  P 31 1 2
pgname    3 1 2 
crysym    trigonal 
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/6
primoper  x,y,z
primoper  -y,x-y,z+1/3
primoper  -x+y,-x,z+2/3
primoper  -y,-x,-z+2/3
primoper  -x+y,y,-z+1/3
primoper  x,x-y,-z
centoper  x,y,z
endofdef


spgid  152
sspgname  P 31 2 1 
fspgname  P 31 2 1
pgname    3 2 1 
crysym    trigonal 
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/6
primoper  x,y,z
primoper  -y,x-y,z+1/3
primoper  -x+y,-x,z+2/3
primoper  y,x,-z
primoper  x-y,-y,-z+2/3
primoper  -x,-x+y,-z+1/3
centoper  x,y,z
endofdef


spgid  153
sspgname  P 32 1 2 
fspgname  P 32 1 2
pgname    3 1 2 
crysym    trigonal 
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/6
primoper  x,y,z
primoper  -y,x-y,z+2/3
primoper  -x+y,-x,z+1/3
primoper  -y,-x,-z+1/3
primoper  -x+y,y,-z+2/3
primoper  x,x-y,-z
centoper  x,y,z
endofdef


spgid  154
sspgname  P 32 2 1 
fspgname  P 32 2 1
pgname    3 2 1 
crysym    trigonal 
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/6
primoper  x,y,z
primoper  -y,x-y,z+2/3
primoper  -x+y,-x,z+1/3
primoper  y,x,-z
primoper  x-y,-y,-z+1/3
primoper  -x,-x+y,-z+2/3
centoper  x,y,z
endofdef

spgid  155
sspgname  R 3 2 
fspgname  R 3 2
pgname    3 2 
crysym    trigonal 
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/2
primoper  x,y,z
primoper  z,x,y
primoper  y,z,x
primoper  -z,-y,-x
primoper  -y,-x,-z
primoper  -x,-z,-y
centoper  x,y,z
endofdef

spgid  155
sspgname  H 3 2 
fspgname  H 3 2
pgname    3 2 
crysym    trigonal 
xyzasu    0<=x<1; 0<=y<=2/3; 0<=z<=1/6
primoper  x,y,z
primoper  -y,x-y,z
primoper  -x+y,-x,z
primoper  y,x,-z
primoper  x-y,-y,-z
primoper  -x,-x+y,-z
centoper  x,y,z
centoper  x+2/3,y+1/3,z+1/3
centoper  x+1/3,y+2/3,z+2/3
endofdef

spgid  156
sspgname  P 3 m 1 
fspgname  P 3 m 1
pgname    3 m 1 
crysym    trigonal 
xyzasu    0<=x<=2/3; 0<=y<=2/3; 0<=z<1
primoper  x,y,z
primoper  -y,x-y,z
primoper  -x+y,-x,z
primoper  -y,-x,z
primoper  -x+y,y,z
primoper  x,x-y,z
centoper  x,y,z
endofdef


spgid  157
sspgname  P 3 1 m 
fspgname  P 3 1 m
pgname    3 1 m 
crysym    trigonal 
xyzasu    0<=x<1; 0<=y<=1/3; 0<=z<1
primoper  x,y,z
primoper  -y,x-y,z
primoper  -x+y,-x,z
primoper  y,x,z
primoper  x-y,-y,z
primoper  -x,-x+y,z
centoper  x,y,z
endofdef


spgid  158
sspgname  P 3 c 1 
fspgname  P 3 c 1
pgname    3 m 1 
crysym    trigonal 
xyzasu    0<=x<1; 0<=y<=2/3; 0<=z<=1/2
primoper  x,y,z
primoper  -y,x-y,z
primoper  -x+y,-x,z
primoper  -y,-x,z+1/2
primoper  -x+y,y,z+1/2
primoper  x,x-y,z+1/2
centoper  x,y,z
endofdef


spgid  159
sspgname  P 3 1 c 
fspgname  P 3 1 c
pgname    3 1 m 
crysym    trigonal 
xyzasu    0<=x<1; 0<=y<=2/3; 0<=z<=1/2
primoper  x,y,z
primoper  -y,x-y,z
primoper  -x+y,-x,z
primoper  y,x,z+1/2
primoper  x-y,-y,z+1/2
primoper  -x,-x+y,z+1/2
centoper  x,y,z
endofdef

spgid  160
sspgname  R 3 m 
fspgname  R 3 m
pgname    3 m 
crysym    trigonal 
xyzasu    0<=x<1; 0<=y<1; 0<=z<1
primoper  x,y,z
primoper  z,x,y
primoper  y,z,x
primoper  z,y,x
primoper  y,x,z
primoper  x,z,y
centoper  x,y,z
endofdef

spgid  160
sspgname  H 3 m 
fspgname  H 3 m
pgname    3 m 
crysym    trigonal 
xyzasu    0<=x<1; 0<=y<2/3; 0<=z<=1/3
primoper  x,y,z
primoper  -y,x-y,z
primoper  -x+y,-x,z
primoper  -y,-x,z
primoper  -x+y,y,z
primoper  x,x-y,z
centoper  x,y,z
centoper  x+2/3,y+1/3,z+1/3
centoper  x+1/3,y+2/3,z+2/3
endofdef

spgid  161
sspgname  R 3 c 
fspgname  R 3 c
pgname    3 m 
crysym    trigonal 
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/2
primoper  x,y,z
primoper  z,x,y
primoper  y,z,x
primoper  z+1/2,y+1/2,x+1/2
primoper  y+1/2,x+1/2,z+1/2
primoper  x+1/2,z+1/2,y+1/2
centoper  x,y,z
endofdef

spgid  161
sspgname  H 3 c 
fspgname  H 3 c
pgname    3 m 
crysym    trigonal 
xyzasu    0<=x<1; 0<=y<2/3; 0<=z<=1/6
primoper  x,y,z
primoper  -y,x-y,z
primoper  -x+y,-x,z
primoper  -y,-x,z+1/2
primoper  -x+y,y,z+1/2
primoper  x,x-y,z+1/2
centoper  x,y,z
centoper  x+2/3,y+1/3,z+1/3
centoper  x+1/3,y+2/3,z+2/3
endofdef

spgid  162
sspgname  P -3 1 m 
fspgname  P -3 1 2/m
pgname    -3 1 m 
crysym    trigonal 
xyzasu    0<=x<1; 0<=y<=1/3; 0<=z<=1/2
primoper  x,y,z
primoper  -y,x-y,z
primoper  -x+y,-x,z
primoper  -y,-x,-z
primoper  -x+y,y,-z
primoper  x,x-y,-z
primoper  -x,-y,-z
primoper  y,-x+y,-z
primoper  x-y,x,-z
primoper  y,x,z
primoper  x-y,-y,z
primoper  -x,-x+y,z
centoper  x,y,z
endofdef


spgid  163
sspgname  P -3 1 c 
fspgname  P -3 1 2/c
pgname    -3 1 m 
crysym    trigonal 
xyzasu    0<=x<1; 0<=y<=2/3; 0<=z<=1/4
primoper  x,y,z
primoper  -y,x-y,z
primoper  -x+y,-x,z
primoper  -y,-x,-z+1/2
primoper  -x+y,y,-z+1/2
primoper  x,x-y,-z+1/2
primoper  -x,-y,-z
primoper  y,-x+y,-z
primoper  x-y,x,-z
primoper  y,x,z+1/2
primoper  x-y,-y,z+1/2
primoper  -x,-x+y,z+1/2
centoper  x,y,z
endofdef


spgid  164
sspgname  P -3 m 1 
fspgname  P -3 2/m 1
pgname    -3 m 1 
crysym    trigonal 
xyzasu    0<=x<1; 0<=y<=2/3; 0<=z<=1/2
primoper  x,y,z
primoper  -y,x-y,z
primoper  -x+y,-x,z
primoper  y,x,-z
primoper  x-y,-y,-z
primoper  -x,-x+y,-z
primoper  -x,-y,-z
primoper  y,-x+y,-z
primoper  x-y,x,-z
primoper  -y,-x,z
primoper  -x+y,y,z
primoper  x,x-y,z
centoper  x,y,z
endofdef


spgid  165
sspgname  P -3 c 1 
fspgname  P -3 2/c 1
pgname    -3 m 1 
crysym    trigonal 
xyzasu    0<=x<1; 0<=y<=2/3; 0<=z<=1/4
primoper  x,y,z
primoper  -y,x-y,z
primoper  -x+y,-x,z
primoper  y,x,-z+1/2
primoper  x-y,-y,-z+1/2
primoper  -x,-x+y,-z+1/2
primoper  -x,-y,-z
primoper  y,-x+y,-z
primoper  x-y,x,-z
primoper  -y,-x,z+1/2
primoper  -x+y,y,z+1/2
primoper  x,x-y,z+1/2
centoper  x,y,z
endofdef

spgid  166
sspgname  R -3 m 
fspgname  R -3 2/m
pgname    -3 m 
crysym    trigonal 
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/2
primoper  x,y,z
primoper  z,x,y
primoper  y,z,x
primoper  -z,-y,-x
primoper  -y,-x,-z
primoper  -x,-z,-y
primoper  -x,-y,-z
primoper  -z,-x,-y
primoper  -y,-z,-x
primoper  z,y,x
primoper  y,x,z
primoper  x,z,y
centoper  x,y,z
endofdef

spgid  166
sspgname  H -3 m 
fspgname  H -3 2/m
pgname    -3 m 
crysym    trigonal 
xyzasu    0<=x<1; 0<=y<=2/3; 0<=z<=1/6
primoper  x,y,z
primoper  -y,x-y,z
primoper  -x+y,-x,z
primoper  y,x,-z
primoper  x-y,-y,-z
primoper  -x,-x+y,-z
primoper  -x,-y,-z
primoper  y,-x+y,-z
primoper  x-y,x,-z
primoper  -y,-x,z
primoper  -x+y,y,z
primoper  x,x-y,z
centoper  x,y,z
centoper  x+2/3,y+1/3,z+1/3
centoper  x+1/3,y+2/3,z+2/3
endofdef

spgid  167
sspgname  R -3 c 
fspgname  R -3 2/c
pgname    -3 m 
crysym    trigonal 
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/4
primoper  x,y,z
primoper  z,x,y
primoper  y,z,x
primoper  -z+1/2,-y+1/2,-x+1/2
primoper  -y+1/2,-x+1/2,-z+1/2
primoper  -x+1/2,-z+1/2,-y+1/2
primoper  -x,-y,-z
primoper  -z,-x,-y
primoper  -y,-z,-x
primoper  z+1/2,y+1/2,x+1/2
primoper  y+1/2,x+1/2,z+1/2
primoper  x+1/2,z+1/2,y+1/2
centoper  x,y,z
endofdef

spgid  167
sspgname  H -3 c 
fspgname  H -3 2/c
pgname    -3 m 
crysym    trigonal 
xyzasu    0<=x<1; 0<=y<=2/3; 0<=z<=1/12
primoper  x,y,z
primoper  -y,x-y,z
primoper  -x+y,-x,z
primoper  y,x,-z+1/2
primoper  x-y,-y,-z+1/2
primoper  -x,-x+y,-z+1/2
primoper  -x,-y,-z
primoper  y,-x+y,-z
primoper  x-y,x,-z
primoper  -y,-x,z+1/2
primoper  -x+y,y,z+1/2
primoper  x,x-y,z+1/2
centoper  x,y,z
centoper  x+2/3,y+1/3,z+1/3
centoper  x+1/3,y+2/3,z+2/3
endofdef

spgid  168
sspgname  P 6 
fspgname  P 6
pgname    6 
crysym    hexagonal 
xyzasu    0<=x<1; 0<=y<=1/3; 0<=z<1
primoper  x,y,z
primoper  -y,x-y,z
primoper  -x+y,-x,z
primoper  -x,-y,z
primoper  y,-x+y,z
primoper  x-y,x,z
centoper  x,y,z
endofdef


spgid  169
sspgname  P 61 
fspgname  P 61
pgname    6 
crysym    hexagonal 
xyzasu    0<=x<1; 0<=y<1; 0<=z<1/6
primoper  x,y,z
primoper  -y,x-y,z+1/3
primoper  -x+y,-x,z+2/3
primoper  -x,-y,z+1/2
primoper  y,-x+y,z+5/6
primoper  x-y,x,z+1/6
centoper  x,y,z
endofdef


spgid  170
sspgname  P 65 
fspgname  P 65
pgname    6 
crysym    hexagonal 
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/6
primoper  x,y,z
primoper  -y,x-y,z+2/3
primoper  -x+y,-x,z+1/3
primoper  -x,-y,z+1/2
primoper  y,-x+y,z+1/6
primoper  x-y,x,z+5/6
centoper  x,y,z
endofdef


spgid  171
sspgname  P 62 
fspgname  P 62
pgname    6 
crysym    hexagonal 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/3
primoper  x,y,z
primoper  -y,x-y,z+2/3
primoper  -x+y,-x,z+1/3
primoper  -x,-y,z
primoper  y,-x+y,z+2/3
primoper  x-y,x,z+1/3
centoper  x,y,z
endofdef


spgid  172
sspgname  P 64 
fspgname  P 64
pgname    6 
crysym    hexagonal 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/3
primoper  x,y,z
primoper  -y,x-y,z+1/3
primoper  -x+y,-x,z+2/3
primoper  -x,-y,z
primoper  y,-x+y,z+1/3
primoper  x-y,x,z+2/3
centoper  x,y,z
endofdef


spgid  173
sspgname  P 63 
fspgname  P 63
pgname    6 
crysym    hexagonal 
xyzasu    0<=x<1; 0<=y<=2/3; 0<=z<=1/2
primoper  x,y,z
primoper  -y,x-y,z
primoper  -x+y,-x,z
primoper  -x,-y,z+1/2
primoper  y,-x+y,z+1/2
primoper  x-y,x,z+1/2
centoper  x,y,z
endofdef


spgid  174
sspgname  P -6 
fspgname  P -6
pgname    -6 
crysym    hexagonal 
xyzasu    0<=x<1; 0<=y<=2/3; 0<=z<=1/2
primoper  x,y,z
primoper  -y,x-y,z
primoper  -x+y,-x,-z
primoper  x,y,-z
primoper  -y,x-y,-z
primoper  -x+y,-x,z
centoper  x,y,z
endofdef


spgid  175
sspgname  P 6/m 
fspgname  P 6/m
pgname    6/m 
crysym    hexagonal 
xyzasu    0<=x<1; 0<=y<=1/3; 0<=z<=1/2
primoper  x,y,z
primoper  -y,x-y,z
primoper  -x+y,-x,z
primoper  -x,-y,z
primoper  y,-x+y,z
primoper  x-y,x,z
primoper  -x,-y,-z
primoper  y,-x+y,-z
primoper  x-y,x,-z
primoper  x,y,-z
primoper  -y,x-y,-z
primoper  -x+y,-x,-z
centoper  x,y,z
endofdef


spgid  176
sspgname  P 63/m 
fspgname  P 63/m
pgname    6/m 
crysym    hexagonal 
xyzasu    0<=x<1; 0<=y<=2/3; 0<=z<=1/4
primoper  x,y,z
primoper  -y,x-y,z
primoper  -x+y,-x,z
primoper  -x,-y,z+1/2
primoper  y,-x+y,z+1/2
primoper  x-y,x,z+1/2
primoper  -x,-y,-z
primoper  y,-x+y,-z
primoper  x-y,x,-z
primoper  x,y,-z+1/2
primoper  -y,x-y,-z+1/2
primoper  -x+y,-x,-z+1/2
centoper  x,y,z
endofdef


spgid  177
sspgname  P 6 2 2 
fspgname  P 6 2 2
pgname    6 2 2 
crysym    hexagonal 
xyzasu    0<=x<1; 0<=y<=1/3; 0<=z<=1/2
primoper  x,y,z
primoper  -y,x-y,z
primoper  -x+y,-x,z
primoper  -x,-y,z
primoper  y,-x+y,z
primoper  x-y,x,z
primoper  y,x,-z
primoper  x-y,-y,-z
primoper  -x,-x+y,-z
primoper  -y,-x,-z
primoper  -x+y,y,-z
primoper  x,x-y,-z
centoper  x,y,z
endofdef


spgid  178
sspgname  P 61 2 2 
fspgname  P 61 2 2
pgname    6 2 2 
crysym    hexagonal 
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/12
primoper  x,y,z
primoper  -y,x-y,z+1/3
primoper  -x+y,-x,z+2/3
primoper  -x,-y,z+1/2
primoper  y,-x+y,z+5/6
primoper  x-y,x,z+1/6
primoper  y,x,-z+1/3
primoper  x-y,-y,-z
primoper  -x,-x+y,-z+2/3
primoper  -y,-x,-z+5/6
primoper  -x+y,y,-z+1/2
primoper  x,x-y,-z+1/6
centoper  x,y,z
endofdef


spgid  179
sspgname  P 65 2 2 
fspgname  P 65 2 2
pgname    6 2 2 
crysym    hexagonal 
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/12
primoper  x,y,z
primoper  -y,x-y,z+2/3
primoper  -x+y,-x,z+1/3
primoper  -x,-y,z+1/2
primoper  y,-x+y,z+1/6
primoper  x-y,x,z+5/6
primoper  y,x,-z+2/3
primoper  x-y,-y,-z
primoper  -x,-x+y,-z+1/3
primoper  -y,-x,-z+1/6
primoper  -x+y,y,-z+1/2
primoper  x,x-y,-z+5/6
centoper  x,y,z
endofdef


spgid  180
sspgname  P 62 2 2 
fspgname  P 62 2 2
pgname    6 2 2 
crysym    hexagonal 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/6
primoper  x,y,z
primoper  -y,x-y,z+2/3
primoper  -x+y,-x,z+1/3
primoper  -x,-y,z
primoper  y,-x+y,z+2/3
primoper  x-y,x,z+1/3
primoper  y,x,-z+2/3
primoper  x-y,-y,-z
primoper  -x,-x+y,-z+1/3
primoper  -y,-x,-z+2/3
primoper  -x+y,y,-z
primoper  x,x-y,-z+1/3
centoper  x,y,z
endofdef


spgid  181
sspgname  P 64 2 2 
fspgname  P 64 2 2
pgname    6 2 2 
crysym    hexagonal 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/6
primoper  x,y,z
primoper  -y,x-y,z+1/3
primoper  -x+y,-x,z+2/3
primoper  -x,-y,z
primoper  y,-x+y,z+1/3
primoper  x-y,x,z+2/3
primoper  y,x,-z+1/3
primoper  x-y,-y,-z
primoper  -x,-x+y,-z+2/3
primoper  -y,-x,-z+1/3
primoper  -x+y,y,-z
primoper  x,x-y,-z+2/3
centoper  x,y,z
endofdef


spgid  182
sspgname  P 63 2 2 
fspgname  P 63 2 2
pgname    6 2 2 
crysym    hexagonal 
xyzasu    0<=x<1; 0<=y<=2/3; 0<=z<=1/4
primoper  x,y,z
primoper  -y,x-y,z
primoper  -x+y,-x,z
primoper  -x,-y,z+1/2
primoper  y,-x+y,z+1/2
primoper  x-y,x,z+1/2
primoper  y,x,-z
primoper  x-y,-y,-z
primoper  -x,-x+y,-z
primoper  -y,-x,-z+1/2
primoper  -x+y,y,-z+1/2
primoper  x,x-y,-z+1/2
centoper  x,y,z
endofdef


spgid  183
sspgname  P 6 m m 
fspgname  P 6 m m
pgname    6 m m 
crysym    hexagonal 
xyzasu    0<=x<1; 0<=y<=1/3; 0<=z<1
primoper  x,y,z
primoper  -y,x-y,z
primoper  -x+y,-x,z
primoper  -x,-y,z
primoper  y,-x+y,z
primoper  x-y,x,z
primoper  -y,-x,z
primoper  -x+y,y,z
primoper  x,x-y,z
primoper  y,x,z
primoper  x-y,-y,z
primoper  -x,-x+y,z
centoper  x,y,z
endofdef


spgid  184
sspgname  P 6 c c 
fspgname  P 6 c c
pgname    6 m m 
crysym    hexagonal 
xyzasu    0<=x<1; 0<=y<=1/3; 0<=z<1/2
primoper  x,y,z
primoper  -y,x-y,z
primoper  -x+y,-x,z
primoper  -x,-y,z
primoper  y,-x+y,z
primoper  x-y,x,z
primoper  -y,-x,z+1/2
primoper  -x+y,y,z+1/2
primoper  x,x-y,z+1/2
primoper  y,x,z+1/2
primoper  x-y,-y,z+1/2
primoper  -x,-x+y,z+1/2
centoper  x,y,z
endofdef


spgid  185
sspgname  P 63 c m 
fspgname  P 63 c m
pgname    6 m m 
crysym    hexagonal 
xyzasu    0<=x<1; 0<=y<=1/3; 0<=z<=1/2
primoper  x,y,z
primoper  -y,x-y,z
primoper  -x+y,-x,z
primoper  -x,-y,z+1/2
primoper  y,-x+y,z+1/2
primoper  x-y,x,z+1/2
primoper  -y,-x,z+1/2
primoper  -x+y,y,z+1/2
primoper  x,x-y,z+1/2
primoper  y,x,z
primoper  x-y,-y,z
primoper  -x,-x+y,z
centoper  x,y,z
endofdef


spgid  186
sspgname  P 63 m c 
fspgname  P 63 m c
pgname    6 m m 
crysym    hexagonal 
xyzasu    0<=x<1; 0<=y<=2/3; 0<=z<=1/2
primoper  x,y,z
primoper  -y,x-y,z
primoper  -x+y,-x,z
primoper  -x,-y,z+1/2
primoper  y,-x+y,z+1/2
primoper  x-y,x,z+1/2
primoper  -y,-x,z
primoper  -x+y,y,z
primoper  x,x-y,z
primoper  y,x,z+1/2
primoper  x-y,-y,z+1/2
primoper  -x,-x+y,z+1/2
centoper  x,y,z
endofdef


spgid  187
sspgname  P -6 m 2 
fspgname  P -6 m 2
pgname    -6 m 2 
crysym    hexagonal 
xyzasu    0<=x<=2/3; 0<=y<=2/3; 0<=z<=1/2
primoper  x,y,z
primoper  -y,x-y,z
primoper  -x+y,-x,z
primoper  x,y,-z
primoper  -y,x-y,-z
primoper  -x+y,-x,-z
primoper  -y,-x,z
primoper  -x+y,y,z
primoper  x,x-y,z
primoper  -y,-x,-z
primoper  -x+y,y,-z
primoper  x,x-y,-z
centoper  x,y,z
endofdef


spgid  188
sspgname  P -6 c 2 
fspgname  P -6 c 2
pgname    -6 m 2 
crysym    hexagonal 
xyzasu    0<=x<1; 0<=y<=2/3; 0<=z<=1/4
primoper  x,y,z
primoper  -y,x-y,z
primoper  -x+y,-x,z
primoper  x,y,-z+1/2
primoper  -y,x-y,-z+1/2
primoper  -x+y,-x,-z+1/2
primoper  -y,-x,z+1/2
primoper  -x+y,y,z+1/2
primoper  x,x-y,z+1/2
primoper  -y,-x,-z
primoper  -x+y,y,-z
primoper  x,x-y,-z
centoper  x,y,z
endofdef


spgid  189
sspgname  P -6 2 m 
fspgname  P -6 2 m
pgname    -6 2 m 
crysym    hexagonal 
xyzasu    0<=x<1; 0<=y<=1/3; 0<=z<=1/2
primoper  x,y,z
primoper  -y,x-y,z
primoper  -x+y,-x,z
primoper  x,y,-z
primoper  -y,x-y,-z
primoper  -x+y,-x,-z
primoper  y,x,-z
primoper  x-y,-y,-z
primoper  -x,-x+y,-z
primoper  y,x,z
primoper  x-y,-y,z
primoper  -x,-x+y,z
centoper  x,y,z
endofdef


spgid  190
sspgname  P -6 2 c 
fspgname  P -6 2 c
pgname    -6 2 m 
crysym    hexagonal 
xyzasu    0<=x<1; 0<=y<=2/3; 0<=z<=1/4
primoper  x,y,z
primoper  -y,x-y,z
primoper  -x+y,-x,z
primoper  x,y,-z+1/2
primoper  -y,x-y,-z+1/2
primoper  -x+y,-x,-z+1/2
primoper  y,x,-z
primoper  x-y,-y,-z
primoper  -x,-x+y,-z
primoper  y,x,z+1/2
primoper  x-y,-y,z+1/2
primoper  -x,-x+y,z+1/2
centoper  x,y,z
endofdef


spgid  191
sspgname  P 6/m m m 
fspgname  P 6/m 2/m 2/m
pgname    6/m m m 
crysym    hexagonal 
xyzasu    0<=x<1; 0<=y<=1/3; 0<=z<=1/2
primoper  x,y,z
primoper  -y,x-y,z
primoper  -x+y,-x,z
primoper  -x,-y,z
primoper  y,-x+y,z
primoper  x-y,x,z
primoper  y,x,-z
primoper  x-y,-y,-z
primoper  -x,-x+y,-z
primoper  -y,-x,-z
primoper  -x+y,y,-z
primoper  x,x-y,-z
primoper  -x,-y,-z
primoper  y,-x+y,-z
primoper  x-y,x,-z
primoper  x,y,-z
primoper  -y,x-y,-z
primoper  -x+y,-x,-z
primoper  -y,-x,z
primoper  -x+y,y,z
primoper  x,x-y,z
primoper  y,x,z
primoper  x-y,-y,z
primoper  -x,-x+y,z
centoper  x,y,z
endofdef


spgid  192
sspgname  P 6/m c c 
fspgname  P 6/m 2/c 2/c
pgname    6/m m m 
crysym    hexagonal 
xyzasu    0<=x<1; 0<=y<=1/3; 0<=z<=1/4
primoper  x,y,z
primoper  -y,x-y,z
primoper  -x+y,-x,z
primoper  -x,-y,z
primoper  y,-x+y,z
primoper  x-y,x,z
primoper  y,x,-z+1/2
primoper  x-y,-y,-z+1/2
primoper  -x,-x+y,-z+1/2
primoper  -y,-x,-z+1/2
primoper  -x+y,y,-z+1/2
primoper  x,x-y,-z+1/2
primoper  -x,-y,-z
primoper  y,-x+y,-z
primoper  x-y,x,-z
primoper  x,y,-z
primoper  -y,x-y,-z
primoper  -x+y,-x,-z
primoper  -y,-x,z+1/2
primoper  -x+y,y,z+1/2
primoper  x,x-y,z+1/2
primoper  y,x,z+1/2
primoper  x-y,-y,z+1/2
primoper  -x,-x+y,z+1/2
centoper  x,y,z
endofdef


spgid  193
sspgname  P 63/m c m 
fspgname  P 63/m 2/c 2/m
pgname    6/m m m 
crysym    hexagonal 
xyzasu    0<=x<1; 0<=y<=1/3; 0<=z<=1/4
primoper  x,y,z
primoper  -y,x-y,z
primoper  -x+y,-x,z
primoper  -x,-y,z+1/2
primoper  y,-x+y,z+1/2
primoper  x-y,x,z+1/2
primoper  y,x,-z+1/2
primoper  x-y,-y,-z+1/2
primoper  -x,-x+y,-z+1/2
primoper  -y,-x,-z
primoper  -x+y,y,-z
primoper  x,x-y,-z
primoper  -x,-y,-z
primoper  y,-x+y,-z
primoper  x-y,x,-z
primoper  x,y,-z+1/2
primoper  -y,x-y,-z+1/2
primoper  -x+y,-x,-z+1/2
primoper  -y,-x,z+1/2
primoper  -x+y,y,z+1/2
primoper  x,x-y,z+1/2
primoper  y,x,z
primoper  x-y,-y,z
primoper  -x,-x+y,z
centoper  x,y,z
endofdef


spgid  194
sspgname  P 63/m m c 
fspgname  P 63/m 2/m 2/c
pgname    6/m m m 
crysym    hexagonal 
xyzasu    0<=x<1; 0<=y<=2/3; 0<=z<=1/4
primoper  x,y,z
primoper  -y,x-y,z
primoper  -x+y,-x,z
primoper  -x,-y,z+1/2
primoper  y,-x+y,z+1/2
primoper  x-y,x,z+1/2
primoper  y,x,-z
primoper  x-y,-y,-z
primoper  -x,-x+y,-z
primoper  -y,-x,-z+1/2
primoper  -x+y,y,-z+1/2
primoper  x,x-y,-z+1/2
primoper  -x,-y,-z
primoper  y,-x+y,-z
primoper  x-y,x,-z
primoper  x,y,-z+1/2
primoper  -y,x-y,-z+1/2
primoper  -x+y,-x,-z+1/2
primoper  -y,-x,z
primoper  -x+y,y,z
primoper  x,x-y,z
primoper  y,x,z+1/2
primoper  x-y,-y,z+1/2
primoper  -x,-x+y,z+1/2
centoper  x,y,z
endofdef


spgid  195
sspgname  P 2 3 
fspgname  P 2 3
pgname    2 3 
crysym    cubic 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  -x,y,-z
primoper  x,-y,-z
primoper  z,x,y
primoper  z,-x,-y
primoper  -z,-x,y
primoper  -z,x,-y
primoper  y,z,x
primoper  -y,z,-x
primoper  y,-z,-x
primoper  -y,-z,x
centoper  x,y,z
endofdef


spgid  196
sspgname  F 2 3 
fspgname  F 2 3
pgname    2 3 
crysym    cubic 
xyzasu    0<=x<1; 0<=y<=1/4; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -x,y,-z
primoper  x,-y,-z
primoper  z,x,y
primoper  z,-x,-y
primoper  -z,-x,y
primoper  -z,x,-y
primoper  y,z,x
primoper  -y,z,-x
primoper  y,-z,-x
primoper  -y,-z,x
centoper  x,y,z
centoper  x,y+1/2,z+1/2
centoper  x+1/2,y,z+1/2
centoper  x+1/2,y+1/2,z
endofdef


spgid  197
sspgname  I 2 3 
fspgname  I 2 3
pgname    2 3 
crysym    cubic 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -x,y,-z
primoper  x,-y,-z
primoper  z,x,y
primoper  z,-x,-y
primoper  -z,-x,y
primoper  -z,x,-y
primoper  y,z,x
primoper  -y,z,-x
primoper  y,-z,-x
primoper  -y,-z,x
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef


spgid  198
sspgname  P 21 3 
fspgname  P 21 3
pgname    2 3 
crysym    cubic 
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/4
primoper  x,y,z
primoper  -x+1/2,-y,z+1/2
primoper  -x,y+1/2,-z+1/2
primoper  x+1/2,-y+1/2,-z
primoper  z,x,y
primoper  z+1/2,-x+1/2,-y
primoper  -z+1/2,-x,y+1/2
primoper  -z,x+1/2,-y+1/2
primoper  y,z,x
primoper  -y,z+1/2,-x+1/2
primoper  y+1/2,-z+1/2,-x
primoper  -y+1/2,-z,x+1/2
centoper  x,y,z
endofdef


spgid  199
sspgname  I 21 3 
fspgname  I 21 3
pgname    2 3 
crysym    cubic 
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/4
primoper  x,y,z
primoper  -x+1/2,-y,z+1/2
primoper  -x,y+1/2,-z+1/2
primoper  x+1/2,-y+1/2,-z
primoper  z,x,y
primoper  z+1/2,-x+1/2,-y
primoper  -z+1/2,-x,y+1/2
primoper  -z,x+1/2,-y+1/2
primoper  y,z,x
primoper  -y,z+1/2,-x+1/2
primoper  y+1/2,-z+1/2,-x
primoper  -y+1/2,-z,x+1/2
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef


spgid  200
sspgname  P m -3 
fspgname  P 2/m -3
pgname    m -3 
crysym    cubic 
xyzasu    0<=x<=1/2; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  -x,y,-z
primoper  x,-y,-z
primoper  z,x,y
primoper  z,-x,-y
primoper  -z,-x,y
primoper  -z,x,-y
primoper  y,z,x
primoper  -y,z,-x
primoper  y,-z,-x
primoper  -y,-z,x
primoper  -x,-y,-z
primoper  x,y,-z
primoper  x,-y,z
primoper  -x,y,z
primoper  -z,-x,-y
primoper  -z,x,y
primoper  z,x,-y
primoper  z,-x,y
primoper  -y,-z,-x
primoper  y,-z,x
primoper  -y,z,x
primoper  y,z,-x
centoper  x,y,z
endofdef


spgid  201
sspgname  P n -3 
fspgname  P 2/n -3
pgname    m -3 
crysym    cubic 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -x,y,-z
primoper  x,-y,-z
primoper  z,x,y
primoper  z,-x,-y
primoper  -z,-x,y
primoper  -z,x,-y
primoper  y,z,x
primoper  -y,z,-x
primoper  y,-z,-x
primoper  -y,-z,x
primoper  -x+1/2,-y+1/2,-z+1/2
primoper  x+1/2,y+1/2,-z+1/2
primoper  x+1/2,-y+1/2,z+1/2
primoper  -x+1/2,y+1/2,z+1/2
primoper  -z+1/2,-x+1/2,-y+1/2
primoper  -z+1/2,x+1/2,y+1/2
primoper  z+1/2,x+1/2,-y+1/2
primoper  z+1/2,-x+1/2,y+1/2
primoper  -y+1/2,-z+1/2,-x+1/2
primoper  y+1/2,-z+1/2,x+1/2
primoper  -y+1/2,z+1/2,x+1/2
primoper  y+1/2,z+1/2,-x+1/2
centoper  x,y,z
endofdef


spgid  202
sspgname  F m -3 
fspgname  F 2/m -3
pgname    m -3 
crysym    cubic 
xyzasu    0<=x<=1/2; 0<=y<=1/4; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -x,y,-z
primoper  x,-y,-z
primoper  z,x,y
primoper  z,-x,-y
primoper  -z,-x,y
primoper  -z,x,-y
primoper  y,z,x
primoper  -y,z,-x
primoper  y,-z,-x
primoper  -y,-z,x
primoper  -x,-y,-z
primoper  x,y,-z
primoper  x,-y,z
primoper  -x,y,z
primoper  -z,-x,-y
primoper  -z,x,y
primoper  z,x,-y
primoper  z,-x,y
primoper  -y,-z,-x
primoper  y,-z,x
primoper  -y,z,x
primoper  y,z,-x
centoper  x,y,z
centoper  x,y+1/2,z+1/2
centoper  x+1/2,y,z+1/2
centoper  x+1/2,y+1/2,z
endofdef


spgid  203
sspgname  F d -3
fspgname  F 2/d -3
pgname    m -3
crysym    cubic
xyzasu    0<=x<1; 0<=y<=1/4; 0<=z<=1/8
primoper  x,y,z
primoper  -x+1/2,-y+1/2,z
primoper  -x+1/2,y,-z+1/2
primoper  x,-y+1/2,-z+1/2
primoper  z,x,y
primoper  z,-x+1/2,-y+1/2
primoper  -z+1/2,-x+1/2,y
primoper  -z+1/2,x,-y+1/2
primoper  y,z,x
primoper  -y+1/2,z,-x+1/2
primoper  y,-z+1/2,-x+1/2
primoper  -y+1/2,-z+1/2,x
primoper  -x+1/4,-y+1/4,-z+1/4
primoper  x+3/4,y+3/4,-z+1/4
primoper  x+3/4,-y+1/4,z+3/4
primoper  -x+1/4,y+3/4,z+3/4
primoper  -z+1/4,-x+1/4,-y+1/4
primoper  -z+1/4,x+3/4,y+3/4
primoper  z+3/4,x+3/4,-y+1/4
primoper  z+3/4,-x+1/4,y+3/4
primoper  -y+1/4,-z+1/4,-x+1/4
primoper  y+3/4,-z+1/4,x+3/4
primoper  -y+1/4,z+3/4,x+3/4
primoper  y+3/4,z+3/4,-x+1/4
centoper  x,y,z
centoper  x,y+1/2,z+1/2
centoper  x+1/2,y,z+1/2
centoper  x+1/2,y+1/2,z
endofdef


spgid  204
sspgname  I m -3 
fspgname  I 2/m -3
pgname    m -3 
crysym    cubic 
xyzasu    0<=x<=1/2; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -x,y,-z
primoper  x,-y,-z
primoper  z,x,y
primoper  z,-x,-y
primoper  -z,-x,y
primoper  -z,x,-y
primoper  y,z,x
primoper  -y,z,-x
primoper  y,-z,-x
primoper  -y,-z,x
primoper  -x,-y,-z
primoper  x,y,-z
primoper  x,-y,z
primoper  -x,y,z
primoper  -z,-x,-y
primoper  -z,x,y
primoper  z,x,-y
primoper  z,-x,y
primoper  -y,-z,-x
primoper  y,-z,x
primoper  -y,z,x
primoper  y,z,-x
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef


spgid  205
sspgname  P a -3 
fspgname  P 21/a -3
pgname    m -3 
crysym    cubic 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x+1/2,-y,z+1/2
primoper  -x,y+1/2,-z+1/2
primoper  x+1/2,-y+1/2,-z
primoper  z,x,y
primoper  z+1/2,-x+1/2,-y
primoper  -z+1/2,-x,y+1/2
primoper  -z,x+1/2,-y+1/2
primoper  y,z,x
primoper  -y,z+1/2,-x+1/2
primoper  y+1/2,-z+1/2,-x
primoper  -y+1/2,-z,x+1/2
primoper  -x,-y,-z
primoper  x+1/2,y,-z+1/2
primoper  x,-y+1/2,z+1/2
primoper  -x+1/2,y+1/2,z
primoper  -z,-x,-y
primoper  -z+1/2,x+1/2,y
primoper  z+1/2,x,-y+1/2
primoper  z,-x+1/2,y+1/2
primoper  -y,-z,-x
primoper  y,-z+1/2,x+1/2
primoper  -y+1/2,z+1/2,x
primoper  y+1/2,z,-x+1/2
centoper  x,y,z
endofdef


spgid  206
sspgname  I a -3 
fspgname  I 21/a -3
pgname    m -3 
crysym    cubic 
xyzasu    0<=x<1; 0<=y<=1/4; 0<=z<=1/4
primoper  x,y,z
primoper  -x+1/2,-y,z+1/2
primoper  -x,y+1/2,-z+1/2
primoper  x+1/2,-y+1/2,-z
primoper  z,x,y
primoper  z+1/2,-x+1/2,-y
primoper  -z+1/2,-x,y+1/2
primoper  -z,x+1/2,-y+1/2
primoper  y,z,x
primoper  -y,z+1/2,-x+1/2
primoper  y+1/2,-z+1/2,-x
primoper  -y+1/2,-z,x+1/2
primoper  -x,-y,-z
primoper  x+1/2,y,-z+1/2
primoper  x,-y+1/2,z+1/2
primoper  -x+1/2,y+1/2,z
primoper  -z,-x,-y
primoper  -z+1/2,x+1/2,y
primoper  z+1/2,x,-y+1/2
primoper  z,-x+1/2,y+1/2
primoper  -y,-z,-x
primoper  y,-z+1/2,x+1/2
primoper  -y+1/2,z+1/2,x
primoper  y+1/2,z,-x+1/2
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef


spgid  207
sspgname  P 4 3 2 
fspgname  P 4 3 2
pgname    4 3 2 
crysym    cubic 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  -x,y,-z
primoper  x,-y,-z
primoper  z,x,y
primoper  z,-x,-y
primoper  -z,-x,y
primoper  -z,x,-y
primoper  y,z,x
primoper  -y,z,-x
primoper  y,-z,-x
primoper  -y,-z,x
primoper  y,x,-z
primoper  -y,-x,-z
primoper  y,-x,z
primoper  -y,x,z
primoper  x,z,-y
primoper  -x,z,y
primoper  -x,-z,-y
primoper  x,-z,y
primoper  z,y,-x
primoper  z,-y,x
primoper  -z,y,x
primoper  -z,-y,-x
centoper  x,y,z
endofdef


spgid  208
sspgname  P 42 3 2 
fspgname  P 42 3 2
pgname    4 3 2 
crysym    cubic 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -x,y,-z
primoper  x,-y,-z
primoper  z,x,y
primoper  z,-x,-y
primoper  -z,-x,y
primoper  -z,x,-y
primoper  y,z,x
primoper  -y,z,-x
primoper  y,-z,-x
primoper  -y,-z,x
primoper  y+1/2,x+1/2,-z+1/2
primoper  -y+1/2,-x+1/2,-z+1/2
primoper  y+1/2,-x+1/2,z+1/2
primoper  -y+1/2,x+1/2,z+1/2
primoper  x+1/2,z+1/2,-y+1/2
primoper  -x+1/2,z+1/2,y+1/2
primoper  -x+1/2,-z+1/2,-y+1/2
primoper  x+1/2,-z+1/2,y+1/2
primoper  z+1/2,y+1/2,-x+1/2
primoper  z+1/2,-y+1/2,x+1/2
primoper  -z+1/2,y+1/2,x+1/2
primoper  -z+1/2,-y+1/2,-x+1/2
centoper  x,y,z
endofdef


spgid  209
sspgname  F 4 3 2 
fspgname  F 4 3 2
pgname    4 3 2 
crysym    cubic 
xyzasu    0<=x<1; 0<=y<=1/4; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -x,y,-z
primoper  x,-y,-z
primoper  z,x,y
primoper  z,-x,-y
primoper  -z,-x,y
primoper  -z,x,-y
primoper  y,z,x
primoper  -y,z,-x
primoper  y,-z,-x
primoper  -y,-z,x
primoper  y,x,-z
primoper  -y,-x,-z
primoper  y,-x,z
primoper  -y,x,z
primoper  x,z,-y
primoper  -x,z,y
primoper  -x,-z,-y
primoper  x,-z,y
primoper  z,y,-x
primoper  z,-y,x
primoper  -z,y,x
primoper  -z,-y,-x
centoper  x,y,z
centoper  x,y+1/2,z+1/2
centoper  x+1/2,y,z+1/2
centoper  x+1/2,y+1/2,z
endofdef


spgid  210
sspgname  F 41 3 2 
fspgname  F 41 3 2
pgname    4 3 2 
crysym    cubic 
xyzasu    0<=x<1; 0<=y<=1/4; 0<=z<=1/8
primoper  x,y,z
primoper  -x,-y+1/2,z+1/2
primoper  -x,y+1/2,-z+1/2
primoper  x,-y,-z
primoper  z,x,y
primoper  z,-x,-y
primoper  -z,-x+1/2,y+1/2
primoper  -z,x+1/2,-y+1/2
primoper  y,z,x
primoper  -y+1/2,z+1/2,-x
primoper  y+1/2,-z,-x+1/2
primoper  -y,-z,x
primoper  y+1/4,x+1/4,-z+1/4
primoper  -y+3/4,-x+1/4,-z+3/4
primoper  y+3/4,-x+1/4,z+3/4
primoper  -y+1/4,x+1/4,z+1/4
primoper  x+1/4,z+1/4,-y+1/4
primoper  -x+1/4,z+1/4,y+1/4
primoper  -x+3/4,-z+1/4,-y+3/4
primoper  x+3/4,-z+1/4,y+3/4
primoper  z+1/4,y+3/4,-x+3/4
primoper  z+1/4,-y+3/4,x+3/4
primoper  -z+3/4,y+3/4,x+1/4
primoper  -z+1/4,-y+1/4,-x+1/4
centoper  x,y,z
centoper  x,y+1/2,z+1/2
centoper  x+1/2,y,z+1/2
centoper  x+1/2,y+1/2,z
endofdef


spgid  211
sspgname  I 4 3 2 
fspgname  I 4 3 2
pgname    4 3 2 
crysym    cubic 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -x,y,-z
primoper  x,-y,-z
primoper  z,x,y
primoper  z,-x,-y
primoper  -z,-x,y
primoper  -z,x,-y
primoper  y,z,x
primoper  -y,z,-x
primoper  y,-z,-x
primoper  -y,-z,x
primoper  y,x,-z
primoper  -y,-x,-z
primoper  y,-x,z
primoper  -y,x,z
primoper  x,z,-y
primoper  -x,z,y
primoper  -x,-z,-y
primoper  x,-z,y
primoper  z,y,-x
primoper  z,-y,x
primoper  -z,y,x
primoper  -z,-y,-x
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef


spgid  212
sspgname  P 43 3 2 
fspgname  P 43 3 2
pgname    4 3 2 
crysym    cubic 
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/8
primoper  x,y,z
primoper  -x+1/2,-y,z+1/2
primoper  -x,y+1/2,-z+1/2
primoper  x+1/2,-y+1/2,-z
primoper  z,x,y
primoper  z+1/2,-x+1/2,-y
primoper  -z+1/2,-x,y+1/2
primoper  -z,x+1/2,-y+1/2
primoper  y,z,x
primoper  -y,z+1/2,-x+1/2
primoper  y+1/2,-z+1/2,-x
primoper  -y+1/2,-z,x+1/2
primoper  y+1/4,x+3/4,-z+3/4
primoper  -y+1/4,-x+1/4,-z+1/4
primoper  y+3/4,-x+3/4,z+1/4
primoper  -y+3/4,x+1/4,z+3/4
primoper  x+1/4,z+3/4,-y+3/4
primoper  -x+3/4,z+1/4,y+3/4
primoper  -x+1/4,-z+1/4,-y+1/4
primoper  x+3/4,-z+3/4,y+1/4
primoper  z+1/4,y+3/4,-x+3/4
primoper  z+3/4,-y+3/4,x+1/4
primoper  -z+3/4,y+1/4,x+3/4
primoper  -z+1/4,-y+1/4,-x+1/4
centoper  x,y,z
endofdef


spgid  213
sspgname  P 41 3 2 
fspgname  P 41 3 2
pgname    4 3 2 
crysym    cubic 
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/8
primoper  x,y,z
primoper  -x+1/2,-y,z+1/2
primoper  -x,y+1/2,-z+1/2
primoper  x+1/2,-y+1/2,-z
primoper  z,x,y
primoper  z+1/2,-x+1/2,-y
primoper  -z+1/2,-x,y+1/2
primoper  -z,x+1/2,-y+1/2
primoper  y,z,x
primoper  -y,z+1/2,-x+1/2
primoper  y+1/2,-z+1/2,-x
primoper  -y+1/2,-z,x+1/2
primoper  y+3/4,x+1/4,-z+1/4
primoper  -y+3/4,-x+3/4,-z+3/4
primoper  y+1/4,-x+1/4,z+3/4
primoper  -y+1/4,x+3/4,z+1/4
primoper  x+3/4,z+1/4,-y+1/4
primoper  -x+1/4,z+3/4,y+1/4
primoper  -x+3/4,-z+3/4,-y+3/4
primoper  x+1/4,-z+1/4,y+3/4
primoper  z+3/4,y+1/4,-x+1/4
primoper  z+1/4,-y+1/4,x+3/4
primoper  -z+1/4,y+3/4,x+1/4
primoper  -z+3/4,-y+3/4,-x+3/4
centoper  x,y,z
endofdef


spgid  214
sspgname  I 41 3 2 
fspgname  I 41 3 2
pgname    4 3 2 
crysym    cubic 
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/8
primoper  x,y,z
primoper  -x+1/2,-y,z+1/2
primoper  -x+1/2,y,-z
primoper  x,-y,-z+1/2
primoper  z,x,y
primoper  z,-x,-y+1/2
primoper  -z+1/2,-x,y+1/2
primoper  -z+1/2,x,-y
primoper  y,z,x
primoper  -y,z+1/2,-x+1/2
primoper  y+1/2,-z+1/2,-x
primoper  -y+1/2,-z,x+1/2
primoper  y+1/4,x+3/4,-z+3/4
primoper  -y+1/4,-x+1/4,-z+1/4
primoper  y+1/4,-x+1/4,z+3/4
primoper  -y+1/4,x+3/4,z+1/4
primoper  x+1/4,z+3/4,-y+3/4
primoper  -x+1/4,z+3/4,y+1/4
primoper  -x+1/4,-z+1/4,-y+1/4
primoper  x+1/4,-z+1/4,y+3/4
primoper  z+3/4,y+1/4,-x+1/4
primoper  z+3/4,-y+3/4,x+1/4
primoper  -z+3/4,y+1/4,x+3/4
primoper  -z+1/4,-y+1/4,-x+1/4
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef


spgid  215
sspgname  P -4 3 m 
fspgname  P -4 3 m
pgname    -4 3 m 
crysym    cubic 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  -x,y,-z
primoper  x,-y,-z
primoper  z,x,y
primoper  z,-x,-y
primoper  -z,-x,y
primoper  -z,x,-y
primoper  y,z,x
primoper  -y,z,-x
primoper  y,-z,-x
primoper  -y,-z,x
primoper  y,x,z
primoper  -y,-x,z
primoper  y,-x,-z
primoper  -y,x,-z
primoper  x,z,y
primoper  -x,z,-y
primoper  -x,-z,y
primoper  x,-z,-y
primoper  z,y,x
primoper  z,-y,-x
primoper  -z,y,-x
primoper  -z,-y,x
centoper  x,y,z
endofdef


spgid  216
sspgname  F -4 3 m 
fspgname  F -4 3 m
pgname    -4 3 m 
crysym    cubic 
xyzasu    0<=x<1; 0<=y<=1/4; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -x,y,-z
primoper  x,-y,-z
primoper  z,x,y
primoper  z,-x,-y
primoper  -z,-x,y
primoper  -z,x,-y
primoper  y,z,x
primoper  -y,z,-x
primoper  y,-z,-x
primoper  -y,-z,x
primoper  y,x,z
primoper  -y,-x,z
primoper  y,-x,-z
primoper  -y,x,-z
primoper  x,z,y
primoper  -x,z,-y
primoper  -x,-z,y
primoper  x,-z,-y
primoper  z,y,x
primoper  z,-y,-x
primoper  -z,y,-x
primoper  -z,-y,x
centoper  x,y,z
centoper  x,y+1/2,z+1/2
centoper  x+1/2,y,z+1/2
centoper  x+1/2,y+1/2,z
endofdef


spgid  217
sspgname  I -4 3 m 
fspgname  I -4 3 m
pgname    -4 3 m 
crysym    cubic 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -x,y,-z
primoper  x,-y,-z
primoper  z,x,y
primoper  z,-x,-y
primoper  -z,-x,y
primoper  -z,x,-y
primoper  y,z,x
primoper  -y,z,-x
primoper  y,-z,-x
primoper  -y,-z,x
primoper  y,x,z
primoper  -y,-x,z
primoper  y,-x,-z
primoper  -y,x,-z
primoper  x,z,y
primoper  -x,z,-y
primoper  -x,-z,y
primoper  x,-z,-y
primoper  z,y,x
primoper  z,-y,-x
primoper  -z,y,-x
primoper  -z,-y,x
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef


spgid  218
sspgname  P -4 3 n 
fspgname  P -4 3 n
pgname    -4 3 m 
crysym    cubic 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -x,y,-z
primoper  x,-y,-z
primoper  z,x,y
primoper  z,-x,-y
primoper  -z,-x,y
primoper  -z,x,-y
primoper  y,z,x
primoper  -y,z,-x
primoper  y,-z,-x
primoper  -y,-z,x
primoper  y+1/2,x+1/2,z+1/2
primoper  -y+1/2,-x+1/2,z+1/2
primoper  y+1/2,-x+1/2,-z+1/2
primoper  -y+1/2,x+1/2,-z+1/2
primoper  x+1/2,z+1/2,y+1/2
primoper  -x+1/2,z+1/2,-y+1/2
primoper  -x+1/2,-z+1/2,y+1/2
primoper  x+1/2,-z+1/2,-y+1/2
primoper  z+1/2,y+1/2,x+1/2
primoper  z+1/2,-y+1/2,-x+1/2
primoper  -z+1/2,y+1/2,-x+1/2
primoper  -z+1/2,-y+1/2,x+1/2
centoper  x,y,z
endofdef


spgid  219
sspgname  F -4 3 c 
fspgname  F -4 3 c
pgname    -4 3 m 
crysym    cubic 
xyzasu    0<=x<1; 0<=y<=1/4; 0<=z<=1/4
primoper  x,y,z
primoper  -x+1/2,-y+1/2,z
primoper  -x+1/2,y+1/2,-z
primoper  x,-y,-z
primoper  z,x,y
primoper  z,-x,-y
primoper  -z+1/2,-x+1/2,y
primoper  -z+1/2,x+1/2,-y
primoper  y,z,x
primoper  -y+1/2,z,-x+1/2
primoper  y,-z+1/2,-x+1/2
primoper  -y,-z,x
primoper  y,x+1/2,z
primoper  -y+1/2,-x,z
primoper  y+1/2,-x,-z
primoper  -y,x+1/2,-z
primoper  x,z+1/2,y
primoper  -x,z+1/2,-y
primoper  -x+1/2,-z,y
primoper  x+1/2,-z,-y
primoper  z+1/2,y,x
primoper  z+1/2,-y+1/2,-x+1/2
primoper  -z,y,-x+1/2
primoper  -z,-y,x+1/2
centoper  x,y,z
centoper  x,y+1/2,z+1/2
centoper  x+1/2,y,z+1/2
centoper  x+1/2,y+1/2,z
endofdef


spgid  220
sspgname  I -4 3 d 
fspgname  I -4 3 d
pgname    -4 3 m 
crysym    cubic 
xyzasu    0<=x<1; 0<=y<1; 0<=z<=1/8
primoper  x,y,z
primoper  -x,-y+1/2,z
primoper  -x,y+1/2,-z+1/2
primoper  x,-y,-z+1/2
primoper  z,x,y
primoper  z,-x,-y+1/2
primoper  -z,-x+1/2,y
primoper  -z,x+1/2,-y+1/2
primoper  y,z,x
primoper  -y,z+1/2,-x+1/2
primoper  y,-z,-x+1/2
primoper  -y+1/2,-z,x+1/2
primoper  y+3/4,x+3/4,z+3/4
primoper  -y+1/4,-x+3/4,z+3/4
primoper  y+1/4,-x+3/4,-z+1/4
primoper  -y+3/4,x+3/4,-z+1/4
primoper  x+3/4,z+3/4,y+3/4
primoper  -x+3/4,z+3/4,-y+1/4
primoper  -x+1/4,-z+3/4,y+3/4
primoper  x+1/4,-z+3/4,-y+1/4
primoper  z+1/4,y+1/4,x+1/4
primoper  z+3/4,-y+1/4,-x+3/4
primoper  -z+1/4,y+1/4,-x+3/4
primoper  -z+1/4,-y+3/4,x+3/4
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef


spgid  221
sspgname  P m -3 m 
fspgname  P m -3 m
pgname    m -3 m 
crysym    cubic 
xyzasu    0<=x<=1/2; 0<=y<=1/2; 0<=z<=1/2
primoper  x,y,z
primoper  -x,-y,z
primoper  -x,y,-z
primoper  x,-y,-z
primoper  z,x,y
primoper  z,-x,-y
primoper  -z,-x,y
primoper  -z,x,-y
primoper  y,z,x
primoper  -y,z,-x
primoper  y,-z,-x
primoper  -y,-z,x
primoper  y,x,-z
primoper  -y,-x,-z
primoper  y,-x,z
primoper  -y,x,z
primoper  x,z,-y
primoper  -x,z,y
primoper  -x,-z,-y
primoper  x,-z,y
primoper  z,y,-x
primoper  z,-y,x
primoper  -z,-y,-x
primoper  -z,y,x
primoper  -x,-y,-z
primoper  x,y,-z
primoper  x,-y,z
primoper  -x,y,z
primoper  -z,-x,-y
primoper  -z,x,y
primoper  z,x,-y
primoper  z,-x,y
primoper  -y,-z,-x
primoper  y,-z,x
primoper  -y,z,x
primoper  y,z,-x
primoper  -y,-x,z
primoper  y,x,z
primoper  -y,x,-z
primoper  y,-x,-z
primoper  -x,-z,y
primoper  x,-z,-y
primoper  x,z,y
primoper  -x,z,-y
primoper  -z,-y,x
primoper  -z,y,-x
primoper  z,-y,-x
primoper  z,y,x
centoper  x,y,z
endofdef


spgid  222
sspgname  P n -3 n 
fspgname  P 4/n -3 2/n
pgname    m -3 m 
crysym    cubic 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -x,y,-z
primoper  x,-y,-z
primoper  z,x,y
primoper  z,-x,-y
primoper  -z,-x,y
primoper  -z,x,-y
primoper  y,z,x
primoper  -y,z,-x
primoper  y,-z,-x
primoper  -y,-z,x
primoper  y,x,-z
primoper  -y,-x,-z
primoper  y,-x,z
primoper  -y,x,z
primoper  x,z,-y
primoper  -x,z,y
primoper  -x,-z,-y
primoper  x,-z,y
primoper  z,y,-x
primoper  z,-y,x
primoper  -z,y,x
primoper  -z,-y,-x
primoper  -x+1/2,-y+1/2,-z+1/2
primoper  x+1/2,y+1/2,-z+1/2
primoper  x+1/2,-y+1/2,z+1/2
primoper  -x+1/2,y+1/2,z+1/2
primoper  -z+1/2,-x+1/2,-y+1/2
primoper  -z+1/2,x+1/2,y+1/2
primoper  z+1/2,x+1/2,-y+1/2
primoper  z+1/2,-x+1/2,y+1/2
primoper  -y+1/2,-z+1/2,-x+1/2
primoper  y+1/2,-z+1/2,x+1/2
primoper  -y+1/2,z+1/2,x+1/2
primoper  y+1/2,z+1/2,-x+1/2
primoper  -y+1/2,-x+1/2,z+1/2
primoper  y+1/2,x+1/2,z+1/2
primoper  -y+1/2,x+1/2,-z+1/2
primoper  y+1/2,-x+1/2,-z+1/2
primoper  -x+1/2,-z+1/2,y+1/2
primoper  x+1/2,-z+1/2,-y+1/2
primoper  x+1/2,z+1/2,y+1/2
primoper  -x+1/2,z+1/2,-y+1/2
primoper  -z+1/2,-y+1/2,x+1/2
primoper  -z+1/2,y+1/2,-x+1/2
primoper  z+1/2,-y+1/2,-x+1/2
primoper  z+1/2,y+1/2,x+1/2
centoper  x,y,z
endofdef


spgid  223
sspgname  P m -3 n 
fspgname  P 42/m -3 2/n
pgname    m -3 m 
crysym    cubic 
xyzasu    0<=x<=1/2; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -x,y,-z
primoper  x,-y,-z
primoper  z,x,y
primoper  z,-x,-y
primoper  -z,-x,y
primoper  -z,x,-y
primoper  y,z,x
primoper  -y,z,-x
primoper  y,-z,-x
primoper  -y,-z,x
primoper  y+1/2,x+1/2,-z+1/2
primoper  -y+1/2,-x+1/2,-z+1/2
primoper  y+1/2,-x+1/2,z+1/2
primoper  -y+1/2,x+1/2,z+1/2
primoper  x+1/2,z+1/2,-y+1/2
primoper  -x+1/2,z+1/2,y+1/2
primoper  -x+1/2,-z+1/2,-y+1/2
primoper  x+1/2,-z+1/2,y+1/2
primoper  z+1/2,y+1/2,-x+1/2
primoper  z+1/2,-y+1/2,x+1/2
primoper  -z+1/2,y+1/2,x+1/2
primoper  -z+1/2,-y+1/2,-x+1/2
primoper  -x,-y,-z
primoper  x,y,-z
primoper  x,-y,z
primoper  -x,y,z
primoper  -z,-x,-y
primoper  -z,x,y
primoper  z,x,-y
primoper  z,-x,y
primoper  -y,-z,-x
primoper  y,-z,x
primoper  -y,z,x
primoper  y,z,-x
primoper  -y+1/2,-x+1/2,z+1/2
primoper  y+1/2,x+1/2,z+1/2
primoper  -y+1/2,x+1/2,-z+1/2
primoper  y+1/2,-x+1/2,-z+1/2
primoper  -x+1/2,-z+1/2,y+1/2
primoper  x+1/2,-z+1/2,-y+1/2
primoper  x+1/2,z+1/2,y+1/2
primoper  -x+1/2,z+1/2,-y+1/2
primoper  -z+1/2,-y+1/2,x+1/2
primoper  -z+1/2,y+1/2,-x+1/2
primoper  z+1/2,-y+1/2,-x+1/2
primoper  z+1/2,y+1/2,x+1/2
centoper  x,y,z
endofdef


spgid  224
sspgname  P n -3 m 
fspgname  P 42/n -3 2/m
pgname    m -3 m 
crysym    cubic 
xyzasu    0<=x<1; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -x,y,-z
primoper  x,-y,-z
primoper  z,x,y
primoper  z,-x,-y
primoper  -z,-x,y
primoper  -z,x,-y
primoper  y,z,x
primoper  -y,z,-x
primoper  y,-z,-x
primoper  -y,-z,x
primoper  y+1/2,x+1/2,-z+1/2
primoper  -y+1/2,-x+1/2,-z+1/2
primoper  y+1/2,-x+1/2,z+1/2
primoper  -y+1/2,x+1/2,z+1/2
primoper  x+1/2,z+1/2,-y+1/2
primoper  -x+1/2,z+1/2,y+1/2
primoper  -x+1/2,-z+1/2,-y+1/2
primoper  x+1/2,-z+1/2,y+1/2
primoper  z+1/2,y+1/2,-x+1/2
primoper  z+1/2,-y+1/2,x+1/2
primoper  -z+1/2,y+1/2,x+1/2
primoper  -z+1/2,-y+1/2,-x+1/2
primoper  -x+1/2,-y+1/2,-z+1/2
primoper  x+1/2,y+1/2,-z+1/2
primoper  x+1/2,-y+1/2,z+1/2
primoper  -x+1/2,y+1/2,z+1/2
primoper  -z+1/2,-x+1/2,-y+1/2
primoper  -z+1/2,x+1/2,y+1/2
primoper  z+1/2,x+1/2,-y+1/2
primoper  z+1/2,-x+1/2,y+1/2
primoper  -y+1/2,-z+1/2,-x+1/2
primoper  y+1/2,-z+1/2,x+1/2
primoper  -y+1/2,z+1/2,x+1/2
primoper  y+1/2,z+1/2,-x+1/2
primoper  -y,-x,z
primoper  y,x,z
primoper  -y,x,-z
primoper  y,-x,-z
primoper  -x,-z,y
primoper  x,-z,-y
primoper  x,z,y
primoper  -x,z,-y
primoper  -z,-y,x
primoper  -z,y,-x
primoper  z,y,x
primoper  z,-y,-x
centoper  x,y,z
endofdef


spgid  225
sspgname  F m -3 m 
fspgname  F 4/m -3 2/m
pgname    m -3 m 
crysym    cubic 
xyzasu    0<=x<=1/2; 0<=y<=1/4; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -x,y,-z
primoper  x,-y,-z
primoper  z,x,y
primoper  z,-x,-y
primoper  -z,-x,y
primoper  -z,x,-y
primoper  y,z,x
primoper  -y,z,-x
primoper  y,-z,-x
primoper  -y,-z,x
primoper  y,x,-z
primoper  -y,-x,-z
primoper  y,-x,z
primoper  -y,x,z
primoper  x,z,-y
primoper  -x,z,y
primoper  -x,-z,-y
primoper  x,-z,y
primoper  z,y,-x
primoper  z,-y,x
primoper  -z,-y,-x
primoper  -z,y,x
primoper  -x,-y,-z
primoper  x,y,-z
primoper  x,-y,z
primoper  -x,y,z
primoper  -z,-x,-y
primoper  -z,x,y
primoper  z,x,-y
primoper  z,-x,y
primoper  -y,-z,-x
primoper  y,-z,x
primoper  -y,z,x
primoper  y,z,-x
primoper  -y,-x,z
primoper  y,x,z
primoper  -y,x,-z
primoper  y,-x,-z
primoper  -x,-z,y
primoper  x,-z,-y
primoper  x,z,y
primoper  -x,z,-y
primoper  -z,-y,x
primoper  -z,y,-x
primoper  z,-y,-x
primoper  z,y,x
centoper  x,y,z
centoper  x,y+1/2,z+1/2
centoper  x+1/2,y,z+1/2
centoper  x+1/2,y+1/2,z
endofdef


spgid  226
sspgname  F m -3 c 
fspgname  F 4/m -3 2/c
pgname    m -3 m 
crysym    cubic 
xyzasu    0<=x<=1/2; 0<=y<=1/4; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -x,y,-z
primoper  x,-y,-z
primoper  z,x,y
primoper  z,-x,-y
primoper  -z,-x,y
primoper  -z,x,-y
primoper  y,z,x
primoper  -y,z,-x
primoper  y,-z,-x
primoper  -y,-z,x
primoper  y+1/2,x+1/2,-z+1/2
primoper  -y+1/2,-x+1/2,-z+1/2
primoper  y+1/2,-x+1/2,z+1/2
primoper  -y+1/2,x+1/2,z+1/2
primoper  x+1/2,z+1/2,-y+1/2
primoper  -x+1/2,z+1/2,y+1/2
primoper  -x+1/2,-z+1/2,-y+1/2
primoper  x+1/2,-z+1/2,y+1/2
primoper  z+1/2,y+1/2,-x+1/2
primoper  z+1/2,-y+1/2,x+1/2
primoper  -z+1/2,y+1/2,x+1/2
primoper  -z+1/2,-y+1/2,-x+1/2
primoper  -x,-y,-z
primoper  x,y,-z
primoper  x,-y,z
primoper  -x,y,z
primoper  -z,-x,-y
primoper  -z,x,y
primoper  z,x,-y
primoper  z,-x,y
primoper  -y,-z,-x
primoper  y,-z,x
primoper  -y,z,x
primoper  y,z,-x
primoper  -y+1/2,-x+1/2,z+1/2
primoper  y+1/2,x+1/2,z+1/2
primoper  -y+1/2,x+1/2,-z+1/2
primoper  y+1/2,-x+1/2,-z+1/2
primoper  -x+1/2,-z+1/2,y+1/2
primoper  x+1/2,-z+1/2,-y+1/2
primoper  x+1/2,z+1/2,y+1/2
primoper  -x+1/2,z+1/2,-y+1/2
primoper  -z+1/2,-y+1/2,x+1/2
primoper  -z+1/2,y+1/2,-x+1/2
primoper  z+1/2,-y+1/2,-x+1/2
primoper  z+1/2,y+1/2,x+1/2
centoper  x,y,z
centoper  x,y+1/2,z+1/2
centoper  x+1/2,y,z+1/2
centoper  x+1/2,y+1/2,z
endofdef


spgid  227
sspgname  F d -3 m 
fspgname  F 41/d -3 2/m
pgname    m -3 m 
crysym    cubic 
xyzasu    0<=x<1; 0<=y<=1/4; 0<=z<=1/8
primoper  x,y,z
primoper  -x,-y+1/2,z+1/2
primoper  -x,y,-z
primoper  x,-y+1/2,-z+1/2
primoper  z,x,y
primoper  z,-x+1/2,-y+1/2
primoper  -z,-x+1/2,y+1/2
primoper  -z,x,-y
primoper  y,z,x
primoper  -y+1/2,z+1/2,-x
primoper  y+1/2,-z,-x+1/2
primoper  -y+1/2,-z+1/2,x
primoper  y+3/4,x+1/4,-z+3/4
primoper  -y+1/4,-x+1/4,-z+1/4
primoper  y+3/4,-x+1/4,z+3/4
primoper  -y+1/4,x+1/4,z+1/4
primoper  x+3/4,z+1/4,-y+3/4
primoper  -x+1/4,z+1/4,y+1/4
primoper  -x+1/4,-z+1/4,-y+1/4
primoper  x+3/4,-z+1/4,y+3/4
primoper  z+1/4,y+3/4,-x+3/4
primoper  z+1/4,-y+1/4,x+1/4
primoper  -z+1/4,-y+3/4,-x+3/4
primoper  -z+3/4,y+1/4,x+3/4
primoper  -x+1/4,-y+1/4,-z+1/4
primoper  x+1/4,y+3/4,-z+3/4
primoper  x+1/4,-y+1/4,z+1/4
primoper  -x+1/4,y+3/4,z+3/4
primoper  -z+1/4,-x+1/4,-y+1/4
primoper  -z+1/4,x+3/4,y+3/4
primoper  z+1/4,x+3/4,-y+3/4
primoper  z+1/4,-x+1/4,y+1/4
primoper  -y+1/4,-z+1/4,-x+1/4
primoper  y+3/4,-z+3/4,x+1/4
primoper  -y+3/4,z+1/4,x+3/4
primoper  y+3/4,z+3/4,-x+1/4
primoper  y,-x,-z
primoper  y,x,z
primoper  -y+1/2,-x,z+1/2
primoper  -y+1/2,x,-z+1/2
primoper  -x+1/2,-z,y+1/2
primoper  x,-z,-y
primoper  x,z,y
primoper  -x+1/2,z,-y+1/2
primoper  -z,-y+1/2,x+1/2
primoper  -z,y,-x
primoper  z+1/2,-y,-x+1/2
primoper  z,y+1/2,x+1/2
centoper  x,y,z
centoper  x,y+1/2,z+1/2
centoper  x+1/2,y,z+1/2
centoper  x+1/2,y+1/2,z
endofdef


spgid  228
sspgname  F d -3 c 
fspgname  F 41/d -3 2/c
pgname    m -3 m 
crysym    cubic 
xyzasu    0<=x<1; 0<=y<=1/4; 0<=z<1/8
primoper  x,y,z
primoper  -x,-y+1/2,z+1/2
primoper  -x+1/2,y+1/2,-z
primoper  x+1/2,-y,-z+1/2
primoper  z,x,y
primoper  z+1/2,-x,-y+1/2
primoper  -z,-x+1/2,y+1/2
primoper  -z+1/2,x+1/2,-y
primoper  y,z,x
primoper  -y+1/2,z+1/2,-x
primoper  y+1/2,-z,-x+1/2
primoper  -y,-z+1/2,x+1/2
primoper  y+3/4,x+1/4,-z+3/4
primoper  -y+1/4,-x+1/4,-z+1/4
primoper  y+1/4,-x+3/4,z+3/4
primoper  -y+3/4,x+3/4,z+1/4
primoper  x+3/4,z+1/4,-y+3/4
primoper  -x+3/4,z+3/4,y+1/4
primoper  -x+1/4,-z+1/4,-y+1/4
primoper  x+1/4,-z+3/4,y+3/4
primoper  z+3/4,y+1/4,-x+3/4
primoper  z+1/4,-y+3/4,x+3/4
primoper  -z+3/4,y+3/4,x+1/4
primoper  -z+1/4,-y+1/4,-x+1/4
primoper  -x+3/4,-y+3/4,-z+3/4
primoper  x+3/4,y+1/4,-z+1/4
primoper  x+1/4,-y+1/4,z+3/4
primoper  -x+1/4,y+3/4,z+1/4
primoper  -z+3/4,-x+3/4,-y+3/4
primoper  -z+1/4,x+3/4,y+1/4
primoper  z+3/4,x+1/4,-y+1/4
primoper  z+1/4,-x+1/4,y+3/4
primoper  -y+3/4,-z+3/4,-x+3/4
primoper  y+1/4,-z+1/4,x+3/4
primoper  -y+1/4,z+3/4,x+1/4
primoper  y+3/4,z+1/4,-x+1/4
primoper  -y,-x+1/2,z
primoper  y+1/2,x+1/2,z+1/2
primoper  -y+1/2,x,-z
primoper  y,-x,-z+1/2
primoper  -x,-z+1/2,y
primoper  x,-z,-y+1/2
primoper  x+1/2,z+1/2,y+1/2
primoper  -x+1/2,z,-y
primoper  -z,-y+1/2,x
primoper  -z+1/2,y,-x
primoper  z,-y,-x+1/2
primoper  z+1/2,y+1/2,x+1/2
centoper  x,y,z
centoper  x,y+1/2,z+1/2
centoper  x+1/2,y,z+1/2
centoper  x+1/2,y+1/2,z
endofdef


spgid  229
sspgname  I m -3 m 
fspgname  I 4/m -3 2/m
pgname    m -3 m 
crysym    cubic 
xyzasu    0<=x<=1/2; 0<=y<=1/2; 0<=z<=1/4
primoper  x,y,z
primoper  -x,-y,z
primoper  -x,y,-z
primoper  x,-y,-z
primoper  z,x,y
primoper  z,-x,-y
primoper  -z,-x,y
primoper  -z,x,-y
primoper  y,z,x
primoper  -y,z,-x
primoper  y,-z,-x
primoper  -y,-z,x
primoper  y,x,-z
primoper  -y,-x,-z
primoper  y,-x,z
primoper  -y,x,z
primoper  x,z,-y
primoper  -x,z,y
primoper  -x,-z,-y
primoper  x,-z,y
primoper  z,y,-x
primoper  z,-y,x
primoper  -z,-y,-x
primoper  -z,y,x
primoper  -x,-y,-z
primoper  x,y,-z
primoper  x,-y,z
primoper  -x,y,z
primoper  -z,-x,-y
primoper  -z,x,y
primoper  z,x,-y
primoper  z,-x,y
primoper  -y,-z,-x
primoper  y,-z,x
primoper  -y,z,x
primoper  y,z,-x
primoper  -y,-x,z
primoper  y,x,z
primoper  -y,x,-z
primoper  y,-x,-z
primoper  -x,-z,y
primoper  x,-z,-y
primoper  x,z,y
primoper  -x,z,-y
primoper  -z,-y,x
primoper  -z,y,-x
primoper  z,-y,-x
primoper  z,y,x
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef


spgid  230
sspgname  I a -3 d 
fspgname  I 41/a -3 2/d
pgname    m -3 m 
crysym    cubic 
xyzasu    0<=x<1; 0<=y<=1/4; 0<=z<=1/8
primoper  x,y,z
primoper  -x+1/2,-y,z+1/2
primoper  -x,y+1/2,-z+1/2
primoper  x+1/2,-y+1/2,-z
primoper  z,x,y
primoper  z+1/2,-x+1/2,-y
primoper  -z+1/2,-x,y+1/2
primoper  -z,x+1/2,-y+1/2
primoper  y,z,x
primoper  -y,z+1/2,-x+1/2
primoper  y+1/2,-z+1/2,-x
primoper  -y+1/2,-z,x+1/2
primoper  y+3/4,x+1/4,-z+1/4
primoper  -y+3/4,-x+3/4,-z+3/4
primoper  y+1/4,-x+1/4,z+3/4
primoper  -y+1/4,x+3/4,z+1/4
primoper  x+3/4,z+1/4,-y+1/4
primoper  -x+1/4,z+3/4,y+1/4
primoper  -x+3/4,-z+3/4,-y+3/4
primoper  x+1/4,-z+1/4,y+3/4
primoper  z+3/4,y+1/4,-x+1/4
primoper  z+1/4,-y+1/4,x+3/4
primoper  -z+1/4,y+3/4,x+1/4
primoper  -z+3/4,-y+3/4,-x+3/4
primoper  -x,-y,-z
primoper  x+1/2,y,-z+1/2
primoper  x,-y+1/2,z+1/2
primoper  -x+1/2,y+1/2,z
primoper  -z,-x,-y
primoper  -z+1/2,x+1/2,y
primoper  z+1/2,x,-y+1/2
primoper  z,-x+1/2,y+1/2
primoper  -y,-z,-x
primoper  y,-z+1/2,x+1/2
primoper  -y+1/2,z+1/2,x
primoper  y+1/2,z,-x+1/2
primoper  -y+1/4,-x+3/4,z+3/4
primoper  y+1/4,x+1/4,z+1/4
primoper  -y+3/4,x+3/4,-z+1/4
primoper  y+3/4,-x+1/4,-z+3/4
primoper  -x+1/4,-z+3/4,y+3/4
primoper  x+3/4,-z+1/4,-y+3/4
primoper  x+1/4,z+1/4,y+1/4
primoper  -x+3/4,z+3/4,-y+1/4
primoper  -z+1/4,-y+3/4,x+3/4
primoper  -z+3/4,y+3/4,-x+1/4
primoper  z+3/4,-y+1/4,-x+3/4
primoper  z+1/4,y+1/4,x+1/4
centoper  x,y,z
centoper  x+1/2,y+1/2,z+1/2
endofdef
