Available versions of this document: latest release, release 3.5, nightly master

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.

### 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:
PermutationAction<Int,Rational>

### 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:
SparseMatrix<Rational,NonSymmetric>

DIM

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

Type:
Int

FACES

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

Type:
Array<Set<Set<Int>>>

FACE_ORBITS

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

Type:
Array<Set<Array<Set<Int>>>>

F_VECTOR

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

Type:
Array<Int>

N_SIMPLICES

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

Type:
Array<Int>

REPRESENTATIVE_INTERIOR_RIDGE_SIMPLICES

The (d-1)-dimensional simplices in the interior.

Type:
Array<Bitset<Int>>

REPRESENTATIVE_MAX_BOUNDARY_SIMPLICES

The boundary (d-1)-dimensional simplices of a cone of combinatorial dimension d

Type:
Array<Bitset<Int>>

REPRESENTATIVE_MAX_INTERIOR_SIMPLICES

The interior d-dimensional simplices of a cone of combinatorial dimension d

Type:
Array<Bitset<Int>>

SIMPLEXITY_LOWER_BOUND

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

Type:
Int

SIMPLICES

All simplices in the quotient space

Type:
Array<Array<Set<Int>>>

SIMPLICIAL_COMPLEX

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

Type:
SimplicialComplex

SYMMETRY_GROUP

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

Type:
Group

• documentation/latest/polytope/quotientspace.txt