documentation:latest:topaz:geometricsimplicialcomplex

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Reference documentation for older polymake versions: release 3.4, release 3.3, release 3.2

# BigObject GeometricSimplicialComplex<Scalar>

from application topaz

A geometric simplicial complex, i.e., a simplicial complex with a geometric realization. Scalar is the numeric data type used for the coordinates.

Type Parameters:

Scalar: default: Rational

derived from:
SimplicialComplex
COORDINATES

Coordinates for the vertices of the simplicial complex, such that the complex is embedded without crossings in some Re. Vector (x1, …. xe) represents a point in Euclidean e-space.

Type:
Matrix<Scalar,NonSymmetric>

G_DIM

Dimension e of the space in which the COORDINATES of the complex is embedded.

Type:
Int

N_UNIMODULAR

Count how many simplices of a geometric simplicial complex are unimodular.

Type:
Int
Example:

Non-regular quadrangle, triangulated.

 > $C = new GeometricSimplicialComplex(COORDINATES=>[[0,0],[1,0],[0,1],[2,1]],FACETS=>[[0,1,2],[1,2,3]]); > print$C->N_UNIMODULAR
1

SIGNATURE

Signature of a geometric simplicial complex embedded in the integer lattice. Like DUAL_GRAPH_SIGNATURE, but only simplices with odd normalized volume are counted.

Type:
Int

UNIMODULAR

A geometric simplicial complex is unimodular if all simplices have unit normalized volume.

Type:
Bool
Example:

Unit square, triangulated.

 > $C = new GeometricSimplicialComplex(COORDINATES=>[[0,0],[1,0],[0,1],[1,1]], FACETS=>[[0,1,2],[1,2,3]]); > print$C->UNIMODULAR
true

VOLUME

Volume of a geometric simplicial complex.

Type:
Scalar

VISUAL()

TODO: consider all inherited user methods; then: user_method … : COORDINATES …

Options:
option list Visual::Polygon::decorations
option list Visual::Graph::decorations

• documentation/latest/topaz/geometricsimplicialcomplex.txt
• Last modified: 2023/11/06 10:57
• by 127.0.0.1