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Reference documentation for older polymake versions: release 3.4, release 3.3, release 3.2
BigObject SubdivisionOfPoints<Scalar>
from application fan
The inhomogeneous variant of SubdivisionOfVectors
, similar to the derivation of PointConfiguration
from VectorConfiguration
.
Properties
Geometry
These properties capture geometric information of the object. Geometric properties depend on geometric information of the object, like, e.g., vertices or facets.

N_POINTS
 Type:

POINTS
The points of the configuration. Multiples allowed. Alias for property
VECTORS
. Type:
Matrix<Scalar,NonSymmetric>

POLYHEDRAL_COMPLEX
The polyhedral complex induced by the cells of the subdivision.
 Type:
PolyhedralComplex<Scalar>

REGULAR
Whether the subdivision is regular, i.e. induced by a weight vector.
 Type:

TIGHT_SPAN
The tight span of the subdivision.
 Type:
PolyhedralComplex<Scalar>

UNIMODULAR
A subdivision is unimodular if it is a triangulation such that each maximal simplex has unit normalized volume.
 Type:
 Example:
Unit square, triangulated.
> $S = new SubdivisionOfPoints(POINTS=>cube(2,0)>VERTICES, WEIGHTS=>[0,0,0,1]); > print $S>UNIMODULAR true
 Example:
Unit 3cube, triangulation induced by four compatible vertex splits.
> $S = new SubdivisionOfPoints(POINTS=>cube(3,0)>VERTICES, WEIGHTS=>[0,1,1,0,1,0,1,0]); > print $S>UNIMODULAR false

WEIGHTS
Vector assigning a weight to each point to get a regular subdivision.
 Type:
Vector<Scalar>
Visualization
These properties are for visualization.

POINT_LABELS
Unique names assigned to the
POINTS
. If specified, they are shown by visualization tools instead of point indices. Alias for propertyLABELS
. Type:
Methods
Geometry
These methods capture geometric information of the object. Geometric properties depend on geometric information of the object, like, e.g., vertices or facets.

AMBIENT_DIM
Ambient dimension of the point configuration (without the homogenization coordinate). Similar to
AMBIENT_DIM
.

DIM
Affine dimension of the point configuration. Similar to
DIM
.

cell(Int i)
Returns the ith cell of the complex as a
PointConfiguration
 Parameters:
Int
i
 Returns:
Visualization
These methods are for visualization.

VISUAL()
Visualizes the
SubdivisionOfPoints
. Options:
 option list
geometric_options
 Returns: