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Reference documentation for older polymake versions: release 3.4, release 3.3, release 3.2
BigObject QuotientSpace
from application polytope
A topological quotient space obtained from a Polytope
by identifying faces. This object will sit inside the polytope.
Properties
Basic properties
Properties defining a quotient space.

IDENTIFICATION_ACTION
The group encoding the quotient space. The faces of the space are the orbits of the faces of the polytope under the group.
 Type:
Combinatorics
These properties capture combinatorial information of the object. Combinatorial properties only depend on combinatorial data of the object like, e.g., the face lattice.

COCIRCUIT_EQUATIONS
a SparseMatrix whose rows are the sum of all cocircuit equations corresponding to a fixed symmetry class of interior ridge
 Type:

DIM
The dimension of the quotient space, defined to be the dimension of the polytope.
 Type:

FACES
The faces of the quotient space, ordered by dimension. One representative of each orbit class is kept.
 Type:

FACE_ORBITS
The orbits of faces of the quotient space, ordered by dimension.
 Type:

F_VECTOR
An array that tells how many faces of each dimension there are
 Type:

N_SIMPLICES
The simplices made from points of the quotient space (also internal simplices, not just faces)
 Type:

REPRESENTATIVE_INTERIOR_RIDGE_SIMPLICES
The (d1)dimensional simplices in the interior.
 Type:

REPRESENTATIVE_MAX_BOUNDARY_SIMPLICES
The boundary (d1)dimensional simplices of a cone of combinatorial dimension d
 Type:

REPRESENTATIVE_MAX_INTERIOR_SIMPLICES
The interior ddimensional simplices of a cone of combinatorial dimension d
 Type:

SIMPLEXITY_LOWER_BOUND
A lower bound for the number of simplices needed to triangulate the quotient space
 Type:

SIMPLICES
All simplices in the quotient space
 Type:

SIMPLICIAL_COMPLEX
A simplicial complex obtained by two stellar subdivisions of the defining polytope.
 Type:

SYMMETRY_GROUP
The symmetry group induced by the symmetry group of the polytope on the
FACES
of the quotient space Type: