There are various means to obtain new objects without having to type the data in a new file manually. Application topaz defines many standard construction and transformation algorithms. Unfortunately, due to the preliminary state of `polymake` reconstruction, we can't supply a uniform, comfortable function-like interface to all of them. At the moment you still have to call the construction clients as separate programs from the shell command line.

## Producing from scratch

With these clients you can create simplicial complexes belonging to various parameterized families.

cube_complex <file> <x_1> <x_2> .. <x_d>
Produces a triangulated pile of hyper cubes: Each cube is split into d! tetrahedra, and the tetrahedra are all grouped around one of the diagonal axes of the cube.
ball <file> <dimension>
Produce a d-ball.
unknot <file> <m> <n> [ <eps> ]
Produces a triangulated 3-sphere with a particular "nasty" embedding of the unknot in its 1-skeleton. The parameters m >= 2 and n >= 1 determine how entangled the unknot is. eps determines the GEOMETRIC_REALIZATION of the unknot.
torus <file>
The torus.
projective_plane <file>
The projective plane.
klein_bottle <file>
The Klein bottle.
sphere <file> <dimension>
Produce a d-sphere.
t_surface <file> <genus>
Produce a surface of genus genus. For genus >= 0 the client produces an orientable surface, otherwise it produces an nonorientable one.
rand_knot <file> <n_edges> [ -n_comp <n> ] [ -on_sphere ] [ -brownian ] [ -precision <digits> ] [ -seed <s> ]
Produce a random knot (or link) as a polygonal closed curve in 3-space. The knot (or each connected component of the link) has n_edges many edges.
The vertices are uniformly distributed in [-1,1]^3, unless the -on_sphere flag is set. In the latter case the vertices are uniformly distributed on the 3-sphere. Alternatively the -brownian flag produces a knot by connecting the ends of a simulated brownian motion.
The default precision is set to 6 digits.

## Producing a new simplicial complex from others

Another important way of constructing simplicial complexes is to modify an already existing one. Actually, these clients don't alter the input file, but create a copy and modify it.

The clients try to preserve existing vertex labels or choose the new labels according to the old ones to help you keep track of special vertices throughout a series of constructions. You may suppress the labeling of the vertices of the new complex by using the -nol flag if it is of no interest to you.

t_star <out_file> <in_file> { -v <v_1> <v_2>...<v_i> ... | -l <l_1> <l_2> ... } [ -nol ]
Produce the star of the face specified by the given vertices.
Vertices can be specified by their indices (using the -v option) or by their labels (using the -l option). Indices may be specified individually or as a sequence. e.g. {1 7...9 20} = {1 7 8 9 20}. (perl lovers might use just two points to indicate a sequence.)
The -nol flag tells the client not to write any labels.
deletion <out_file> <in_file> { -v <v_1> <v_2>...<v_i> ... | -l <l_1> <l_2> ... } [ -nol ]
Removes the vertex star of a given face, specified by it's vertices.
Vertices can be specified by their indices (using the -v option) or by their labels (using the -l option). Indices may be specified individually or as a sequence. e.g. {1 7...9 20} = {1 7 8 9 20}. (perl lovers might use just two points to indicate a sequence.)
The -nol flag tells the client not to write any labels.
t_union <out_file> <in_file_1> <in_file_2> [ -nol ]
Produce the union of the two given complexes, identifying vertices with equal labels.
The -nol flag tells the client not to write any labels.
h_induced_quotient <out_file> <in_file> [ apex ] { -v <v_1> <v_2>...<v_i> ... | -l <l_1> <l_2> ... } [ -nol ]
Let C be the given simplicial complex and A the subcomplex induced by the given vertices. Then this client produces a simplicial complex homotopy equivalent to C mod A, by adding the cone over A with apex a to C.
The apex a may be specified (by its label) and vertices can be specified by their indices (using the -v option) or by their labels (using the -l option). Indices may be specified individually or as a sequence. e.g. {1 7...9 20} = {1 7 8 9 20}. (perl lovers might use just two points to indicate a sequence.)
The -nol flag tells the client not to write any labels.
induced_subcomplex <out_file> <in_file> { -v <v_1> <v_2>...<v_i> ... | -l <l_1> <l_2> ... } [ -geom_real ] [ -nol ]
Produce the subcomplex consisting of all faces which are contained in the given vertices.
Vertices can be specified by their indices (using the -v option) or by their labels (using the -l option). Indices may be specified individually or as a sequence. e.g. {1 7...9 20} = {1 7 8 9 20}. (perl lovers might use just two points to indicate a sequence.)
The -nol flag tells the client not to write any labels.
The -geom_real flag tells the client to inherit the GEOMETRIC_REALIZATION.
bistellar <file1> <file2> [ -rounds <r> ] [ -abs ] [ -obj {0|1|2} ] [ -relax <r> ] [ -heat <h> ] [ -constant ] [ -allow_rev_move ] [ -min_n_facets <n> ] [ -verbose <r> ] [ -seed <s> ] [ -pl_comp ] [ -quiet ] [ -distribution s_(dim+1)/2 .. s_dim ]
Heuristic for simplifying the triangulation of the given manifold without changing its PL-type. The client uses bistellar flips and a simulated annealing strategy.
In the default case, file1 is the output file, and file2 the input. In case the -pl_comp flag is set, both files are input files and the client tries to determine whether file2 is pl-homeomorphic to file1. Here file1 is assumed to be facet minimal.
You may specify the maximal number of -rounds, how often the system may -relax before heating up and how much -heat should be applied. The client stops computing, once the size of the triangulation has not decreased for -rounds iterations. If the -abs flag is set, the client stops after -rounds iterations regardless of when the last improvement took place. Additionally, you may set the threshold -min_n_facets for the number of facets when the simplification ought to stop. Default is d+2 in the CLOSED_PSEUDO_MANIFOLD case and 1 otherwise.
If you want to influence the distribution of the dimension of the moves when warming up you may do so by specifying a -distribution. The number of values in -distribution determine the dimensions used for heating up. The heating and relaxing parameters decrease dynamically unless the -constant flag is set. The client prohibits to execute the reversed move of a move directly after the move itself unless the -allow_rev_move flag is set. Setting the -allow_rev_move flag might help solve a particular resilient problem.
If you are interested in how the process is coming along, try the -verbose option. It specifies after how many rounds the current best result is displayed.
The -obj determines the objective function used for the optimization. If -obj is set to 0, the client searches for the triangulation with the lexicographically smallest f-vector, if -obj is set to 1, the client searches for the triangulation with the reversed-lexicographically smallest f-vector and if -obj is set to 2 the sum of the f-vector entries is used. The default is 1.
t_join <out_file> <in_file_1> <in_file_2> [ -nol ]
Produce the join of the two given complexes.
The vertex labels are built from the original labels with a suffix _1 or _2 appended.
The -nol flag tells the client not to write any labels.
t_balanced_prism <out_file> <in_file> [ -geom_real ]
Produce a prism over a given simplicial complex.
edge_contraction <out_file> <in_file> [ <seed> ]
Heuristic for simplifying the triangulation of the given manifold without changing its PL-type. Choosing a random order of the vertices, the client tries to contract all incident edges.
suspension <out_file> <in_file> <in_complex_section> [ <k> ] [ -l <l_1+> <l_1-> <l_2+> <l_2-> ... ] [ -nol ]
Produce the k-suspension over a given simplicial complex.
Default for the parameter k is 1.
The labels of the apexes may be specified. In case too few apexes are specified the client labels the remaining ones apex_0+, apex_0-, apex_1+, apex_1-, ... . In case one of the labels exists already, the client chooses a unique one by appending _i where i is the smallest integer which makes the label unique.
The -nol flag tells the client not to write any labels.
t_link <out_file> <in_file> { -v <v_1> <v_2>...<v_i> ... | -l <l_1> <l_2> ... } [ -nol ]
Produce the link of the face specified by the given vertices.
Vertices can be specified by their indices (using the -v option) or by their labels (using the -l option). Indices may be specified individually or as a sequence. e.g. {1 7...9 20} = {1 7 8 9 20}. (perl lovers might use just two points to indicate a sequence.)
The -nol flag tells the client not to write any labels.
glue_induced_subcomplexes <out_file> <in_file> <glueing_section> [ -nol ]
The new complex is produced by replacing all vertices from each glueing set by one representative and removing all redundancies.
The glueing sets have to be stored in a separate file section glueing_section as an array of sets of vertex indices. If two sets are not disjoint, their union serves as a single glueing set instead, thus providing transitivity. Vertices not contained in any glueing set are considered to be in a glueing set by themselves, therefore will not be glued at all.
The labels of the new vertices are the original labels of the representative vertices (that is, with the smallest index) of their glueing sets.
The -nol flag skips the label creation.
barycentric_subdivision <out_file> <in_file> [ -relabel ] [ -geom_real ]
Create a simplicial complex as a barycentric subdivision of a given complex. Each vertex in the new complex corresponds to a face in the old complex.
The option -relabel creates an additional section VERTEX_LABELS. The labels are, most naturally, the faces of the original complex.
The option -geom_real reads the GEOMETRIC_REALIZATION of the input complex, computes the coordinates of the new vertices and stores them in
GEOMETRIC_REALIZATION of the produced complex.
disjoint_union <out_file> <in_file_1> <in_file_2> [ -nol ]
Produce the union of the two given complexes.
The vertex labels are built from the original labels with a suffix _1 or _2 appended.
The -nol flag skips the label generation.
k_skeleton <out_file> <in_file> <k> [ -geom_real ] [ -nol ]
Produce the k-skeleton.
The -nol flag tells the client not to write any labels.
stellar_subd_face <out_file> <in_file> { -v <v_1> <v_2>...<v_i> ... | <faces_section> } [ -nol ] [ -geom_real ]
Stellar subdivides either the face specified by the command line input or all faces specified in the <faces_section>.
t_simplicial_product <out_file> <in_file_1> <in_file_2> [ <vertex_order_section1> [ <vertex_order_section1> ] ] [ -nol ] [ -geom_real ] [ -collor_cons ]
Computes the simplicial product of two complexes.
Vertexorderings may be given by specifying sections.
cone <out_file> <in_file> <in_complex_section> [ <k> ] [ -l <l_1> <l_2> ... ] [ -nol ]
Produce the k-cone over a given simplicial complex.
Default for the parameter k is 1.
The option -l specifies how to label the apex vertices. Default labels have the form `apex_0, apex_1, ...` . In the case the input complex has already vertex labels of this kind, the duplicates are avoided.
The -nol flag tells the client not to write any labels at all.
extract_subcomplex <out_file> <in_file> <subcomplex_section> [ -geom_real ] [ -nol ]
Extracts a subcomplex of a given complex and creates a new complex. The indices of the selected vertices have to be stored as an ordered set in a separate file section subcomplex_section.
The vertex labels are preserved unless the -nol flag is specified.
The -geom_real flag tells the client to inherit the GEOMETRIC_REALIZATION.
knot_complex <out_file> <in_file>
Produce a triangulation of the 3-sphere with a given knot (or link) embedded in the 1-skeleton. The realization of the knot in 3-space is assumed to be generic, that is, after projection to the xy-plane at most two edges cross in one point, and any vertex lies in exactly two edges. Parallel edges however are admissible. Further we assume that the projection has at least one crossing and that (in the case of a link) it is connected. The client DOES NOT TEST the latter assumption
alexander_dual <out_file> <in_file> [ -nol ]
Computes the Alexander dual complex, that is the complements of all non-faces.
The vertex labels are preserved unless the -nol flag is specified.
connected_sum <out_file> <in_file_1> <in_file_2> [ <f_1> [ <f_2> ] ] [ -p <p_1> ... <p_n> ] [ -nol ]
Compute the connected sum of two complexes.
Parameters f_1 and f_2 specify which facet of the first and second complex correspondingly are glued together. Default is the 0-th facet of both.
The vertices in the selected facets are identified with each other according to their order in the facet (that is, in icreasing index order). The option -p allows to get an alternative identification. It should specify a permutation of the vertices of the second facet. If the permutation contains contiguous sequences, they can be shortened as n_1 ... n_2 (perl lovers might use just two points.) For example, (7 2 ... 4 12) = (7 2 3 4 12).
The vertices of the new complex get the original labels with _1 or _2 appended, according to the input complex they came from. If you specify the -nol flag, the label generation will be omitted.

## Consistency checks

labels_consistency <file>
Verifies whether the VERTEX_LABELS are unique and that their size matches N_VERTICES
facets_consistency <file> [ <complex_section> [ -auto ] ]
Verifies whether a complex has any redundandent facets, whether the facets are ordered sets and if the vertices are numbered 0..n-1.
The default for the complex_section is FACETS.
If the -auto flag is set the client writes the correct facets into FACETS and the old numbering (if the numbering has changed at all) into VERTEX_LABELS. The complex_section must not equal FACETS.

## Other

is_vert_dec <file> <shedding_vertices_section>
Check whether a given ordered subset of the vertex set is a vertex decomposition.
The client works for 1-, 2- and 3-manifolds only!
projectivities <file> <proj_orbits_section> <proj_dictionary_section>
Computes the orbits of the group of projectivities.

## Producing a simplicial complex from other objects

triangulation_complex <out_file> <in_file> [ -noc ]
Produce the complex which arises out of a triangulation of the polytope.
If the -noc flag is set, no coordinates for the GEOMETRIC_REALIZATION will be written.
This client lives in between the applications poly and topaz. Since it produces a simplicial complex (from a polytope), it is counted as a client for the topaz application.
boundary_complex <out_file> <in_file> [ -noc ]
Produce the boundary complex which arises out of a triangulation of the boundary of polytope.
If the -noc flag is set, no coordinates for the GEOMETRIC_REALIZATION will be written.
This client lives in between the applications poly and topaz. Since it produces a simplicial complex (from a polytope), it is counted as a client for the topaz application.
surf2top <out_file> <in_file> [ -noc ] [ -nol ]
Produce a simplicial complex from a surface by triangulating each n-gon.
If the -noc flag is set, no coordinates for the GEOMETRIC_REALIZATION will be written.
This client lives in between the applications surface and topaz. Since it produces a simplicial complex (from a surface), it is counted as a client for the topaz application.
crosscut_complex <out_file> <in_file> [ -noc ]
Produce the crosscut complex which arises out of a triangulation of the boundary of polytope.
If the -noc flag is set, no coordinates for the GEOMETRIC_REALIZATION will be written.
This client lives in between the applications poly and topaz. Since it produces a simplicial complex (from a polytope), it is counted as a client for the topaz application.
flag_complex <out_file> <in_file> <graph_section> [ -nol ]
Produce the flag_complex of a given graph.
The -nol flag tells the client not to write any labels.

## Clients for internal use

These clients are called by `polymake` automatically via the rules. They compute some new properties of an object. You will hardly ever need to call them directly. They are documented here first of all for the sake of completeness.

triangle_free <file> <graph_section> <triangle_free_section>
Determine whether a (possibly directed) graph has triangles or not.
connected <file> <graph_section> <connected_section>
Determine whether an undirected graph is connected.
induced_subgraph <file> <graph_section> <subgraph_nodes_section> <subgraph_section> [ -nol ] [ -compl ]
Compute the subgraph induced by a given set of nodes.
The nodes are labeled with the original node indices, unless nol option is specified. If compl option is specified, the complement of the subgraph_nodes_section is used to select the subgraph nodes.
se_interactive <file> <port> [ -z-ordering <objective_section> -read-edge-weights -seed <s> -max-iterations <n> ] [ {-scale,-balance,-viscosity,-inertion,-eps,-z-factor} <x> ... ]
Driver for interactive graph visualization
greedy_coloring <file> <graph_section> <coloring_section>
Computes a coloring.
max_cliques <file> <max_cliques_section> <graph_section>
Computes all inclusion maximal cliques of a graph.
isomorphic_graphs <file1> <graph_section1> <file2> <graph_section2> [ <result_section> ]
Determine whether two given graphs are isomorphic.
The answer is written as a boolean property result_section of the first file. If the result section is omitted, prints the node permutation to the standard output.
connectivity <file> <graph_section> <connectivity_section>
Compute the connectivity of a given graph using the Ford-Fulkerson flow algorithm.
Responsible author: Nikolaus Witte
connected_comp <file> <graph_section> <connected_comp_section>
Computes the connected components. The connected components are encoded by their node sets.
hd_embedder <file> <hd_section> <embedding_section> <label_width_section> { -primal | -dual } [ -seed <s> -eps <x> ]
Create an embedding of the Hasse diagram as a layered graph.
The embedding algorithm tries to minimize the weighted sum of squares of edge lengths, starting from a random distribution. The weights are relative to the fatness of the layers.
The y-space between the layers is constant; in the -primal mode the whole-lattice node is placed on the top, in the -dual mode it is the empty node.
label_width_section should contain estimates (better upper bounds) of the label width of each node. The computed layout guarantees that the distances between the nodes in a layer are at least equal to the widest label in this layer.
-eps is the calculation accuracy.
option -seed effects the initial placement of the nodes.
bipartite <file> <graph_section> <bipartite_section> [ <signature_section> ]
Determine whether an undirected graph is bipartite.
Responsible author: Niko Witte
edge_lengths <file> <coords_section> <graph_section> <result_section> [ -redirect ]
Compute the lenghts of all edges of a given graph with assigned coordinates for the nodes. If the -redirect option is set then it is assumed that the graph has indices as node attributes which point into the coordinate section.
spring_embedder <file> <graph_section> <embedding_section> [ -z-ordering <objective_section> -read-edge-weights -seed <s> -max-iterations <n> ] [ {-scale,-balance,-viscosity,-inertion,-eps,-z-factor} <x> ... ]
Produce a 3-d embedding for the graph using the spring embedding algorithm along the lines of

> Thomas Fruchtermann and Edward Reingold:
> Graph Drawing by Force-directed Placement.
> Software Practice and Experience Vol. 21, 1129-1164 (1992), no. 11

The initial node coordinates are chosen randomly on the unit sphere. The optional parameter -seed controls the initial setting.
In the standard setting, the embedding algorithm tries to stretch all edges to the same length. If you prefer different edge lengths, store them as the edge attributes of the input graph, and put the -read-edge-weights option on the command line.
If the nodes already have an embedding in Rd and there is a linear or abstract objective function defined in the coordinate space, it can be used to rearrange the 3-d embedding along the z-axis corresponding to the objective function growth. This mode is enabled with option -z-ordering.
The embedding algorithm can be fine-tuned with several "black magic" options. All of them take double values, which are multiplied with internal initial settings, so all defaults are equal to 1.
-scale enlarges the ideal edge length. -balance changes the balance between the edge contraction and node repulsion forces. -inertion and -viscosity affects how the nodes are moved, and can be used to restrain oscillations. -z-factor changes the relative influence of the objective function on the embedding. -eps controls how far a point may move, to be considered standing still.
diameter <file> <graph_section> <diameter_section>
Compute the diameter of an undirected graph.
orientation <file>
Determines whether a PSEUDO_MANIFOLD is orientable and computes a consistent orientation.
morse_matching <file> [ {-greedy, -cancel, -both} {-top, -bottom, -bottomtop} ]
Input: simplicial complex given by its Hasse diagram
Output: a Morse matching
This client computes a Morse matching. Two heuristics are implemented:

- A simple greedy algorithm: The arcs are visited in lexicographical order, i.e.:
  we proceed by levels from top to bottom, visit the faces in each dimension in lexicographical order, and visited the faces covered by these faces in lexicographical order.
  This heuristic is used with no options and with -greedy.
- A Morse matching can be improved by canceling critical cells along unique alternating paths, see function processAlternatingPaths() in file morse_matching_tools.h . This idea is due to Robin Forman:

  > Morse Theory for Cell-Complexes,
  > Advances in Math., 134 (1998), pp. 90-145.

  This heuristic is used with no options and with -cancel.

The default setting is to run the greedy algorithm and then improve the result by the canceling algorithm, i.e., option -both is the default.
Morse matchings for the bottom level can be found optimally by spanning tree techniques. This can be enabled by the option -bottom. If the complex is a pseudo-manifold the same can be done for the top level (option -top). By specifying option -bottomtop, both levels can be computed by spanning trees. For 2-dim pseudo-manifolds this computes an optimal Morse matching.
Contributed by Marc Pfetsch
minimal_non_faces <file>
Find the inclusion-minimal non-faces of a complex.
stiefel_whitney <file> <out_section> [-v] [<dim_low> [<dim_high>]]
Computes Stiefel-Whitney classes of mod 2 Euler space (in particular, closed manifold). Use option "-v" to show regular pairs and cycles.
A narrower dimension range of interest can be specified. Negative values are treated as co-dimension - 1.
is_pseudo_manifold <file> [ -verbose ]
Check whether a complex is a pseudo_manifold.
t_mixed_graph <file> [ -edge_weight <mixed_edge_weight> ]
Produces the mixed graph of a simplicial complex.
is_ball <file>
Check whether a complex is a ball. The client works for balls of dim 2 or smaller only.
t_signature <file>
Determine the signature of a embedded simplicial complex.
Responsible author: Niko Witte
is_sphere <file>
Check whether a complex is a sphere. The client works for spheres of dim 2 or smaller only.
facets_from_hasse_diagram <file>
Extracts the facets of a hasse diagram
t_staircase <file> <m> <n>
Produce the staircase triangulation of the product of simplices Delta_m x Delta_n.
fundamental_group <file>
Calculate a finite representation of the fundamental group, which may easily be treated with GAP.
is_ball_or_sphere <file>
Check whether a complex is a ball or sphere. The client works for manifolds of dim 2 or smaller only.
is_manifold <file> [ -quiet ]
Check whether a complex is a manifold. The client works for manifolds of dim 3 or smaller only.
morse_matching_critical_faces <file>
Input: Morse matching
Output: list of critical faces and for each dimension: number of critical faces
Contributed by Marc Pfetsch
lawler <file>
Produces the minimal (with respect to inclusion) non-faces of a simplicial complex. Only the facets of the complex are used as input, i.e., no hasse diagram is computed.
This implements an old algorithm described by Lawler: "Covering problems: duality relations and a new method of solution" SIAM J. Appl. Math., Vol. 14, No. 5, 1966
See also Chapter 2 of "Hypergraphs", C. Berge, North-Holland, Amsterdam, 1989
8/23/2002
t_volume <file>
Compute the volume of a simplicial complex.
isomorphic_complexes <file1> <file2> [ <result_section> ]
Determine whether two given complexes are combinatorially isomorphic.
The answer is written as a boolean property result_section of the first file. If the result section is omitted, prints the vertex and facet permutations to the standard output.
is_manifold_h <file> [ -seed <s> ] [ -strategy {0|1} ] [ -stable_rounds <r> ] [ -quiet ] [ -all ]
Heuristic to determin if a complex is a manifold.
morse_matching_n_critical_faces <file>
Input: Morse matching
Output: number of critical cells in Morse matching
Contributed by Marc Pfetsch
odd_complex <file>
Find all faces of co-dimension -2 which have a non bipartied link.
is_ball_h <file> [ -seed <s> ] [ -strategy {0|1} ] [ -stable_rounds <r> ] [ -quiet ]
Heuristic to determin if a complex is a ball.
is_sphere_h <file> [ -seed <s> ] [ -strategy {0|1} ] [ -stable_rounds <r> ] [ -quiet ]
Heuristic to determin if a complex is a sphere.
t_f_vector <file>
Produce the f-vector of a simplicial complex.
boundary_of_pseudo_manifold <file> <boundary_section>
Produce the boundary (= ridges contained in one facet only) of a PSEUDO_MANIFOLD.
is_closed_pseudo_manifold <file>
Check whether a complex is a closed pseudo-manifold.
faces_to_facets <file> <input_section>
Consistency check and redundancy removal.
is_ball_or_sphere_h <file> [ -seed <s> ] [ -strategy {0|1} ] [ -stable_rounds <r> ] [ -quiet ]
Heuristic to determin if a complex is a ball or a ball or a sphere.
t_hasse_diagram <file> [ -pure ]
Produce the Hasse Diagram of a simplicial complex.
intersection_form <file> <cycle_section> <cocycle_section> <intersection_form_section>
Calculate the parity and the signature of the intersection form of an oriented 4-manifold.
t_homology <file> <complex_section> <homology_section> [-co] [ <cycle_section> | <dim_high> <dim_low> ]
Calculate the homology groups and, optionally, cycle representatives of a simplicial complex.
A narrower dimension range of interest can be specified. Negative values are treated as co-dimension - 1.
With option -co, cohomologies and cocycles will be computed.
t_graph <file>
Produces the graph of a simplicial complex.
is_locally_strongly_connected <file> [ -all ] [ -quiet ]
Check whether a complex is locally strongly connected.
The -all flag tells the client to compute all faces with non strongly connected star.
morse_matching_size <file>
Input: Morse matching
Output: size of the Morse matching
Contributed by Marc Pfetsch
t_dual_graph <file>
Produce the dual graph of a simplicial complex.
odd_complex_of_manifold <file>
Find all faces of co-dimension -2 of which have a non bipartied link.