The application polytope defines the following object types:

FloatPolytope, Polytope, RationalPolytope, SchlegelDiagram, TightSpan

Each type is accompanied with alphabetically sorted lists of properties and public methods, both own and inherited from parent types. The items are links to the detailed descriptions.

Underlined is the default type for this application.

The methods inherited from Poly::Object are described on a separate page, as they are only needed for advanced scripting.


Polytope
A realized Polyhedron
properties:
ABSTRACT_OBJECTIVE FACET_SIZES POINTS_IN_FACETS
AFFINE_HULL FACE_SIMPLICITY POSITIVE
ALTSHULER_DET FAR_FACE RANDOM_EDGE_EPL
AMBIENT_DIM FAR_HYPERPLANE REL_INT_POINT
BALANCE FATNESS REVERSE_TRANSFORMATION
BALANCED FEASIBLE SCHLEGEL_PARAMS
BOUNDED FLAG_VECTOR SIMPLE
BOUNDED_GRAPH FTV_CYCLIC_NORMAL SIMPLICIAL
BOUNDING_BOX F_VECTOR SIMPLICIALITY
CD_INDEX_COEFFICIENTS GALE_TRANSFORM SIMPLICITY
CENTERED GALE_VERTICES SITES
CHIROTOPE GRAPH SITE_LABELS
CHIROTOPE_INT HASSE_DIAGRAM STEINER_POINTS
COCUBICAL H_VECTOR TRIANGLE_FREE
COCUBICALITY INEQUALITIES TRIANGULATION
COMPLEXITY ITERATED_DELAUNAY_GRAPH TRIANGULATION_BOUNDARY
CONNECTIVITY ITERATED_VORONOI_GRAPH TRIANGULATION_INT
CRUST_GRAPH LINEAR_OBJECTIVE TRIANGULATION_INT_SIGNS
CUBICAL MAXIMAL_FACE TRIANGULATION_SIGNS
CUBICALITY MAXIMAL_VALUE UNBOUNDED_FACETS
CUBICAL_H_VECTOR MAXIMAL_VERTEX VALID_POINT
DELAUNAY_GRAPH MINIMAL_FACE VARIABLE_NAMES
DIAMETER MINIMAL_VALUE VERTEX_BARYCENTER
DIM MINIMAL_VERTEX VERTEX_COLORS
DIRECTED_GRAPH NEIGHBORLINESS VERTEX_DEGREES
DUAL_CONNECTIVITY NEIGHBORLY VERTEX_IN_DEGREES
DUAL_DIAMETER NEIGHBOR_FACETS_CYCLIC_NORMAL VERTEX_LABELS
DUAL_EVEN NEIGHBOR_VERTICES_CYCLIC_NORMAL VERTEX_NORMALS
DUAL_GRAPH N_BOUNDED_VERTICES VERTEX_OUT_DEGREES
DUAL_TRIANGLE_FREE N_EDGES VERTEX_SIZES
EQUATIONS N_FACETS VERTICES
ESSENTIALLY_GENERIC N_POINTS VERTICES_IN_FACETS
EVEN N_RIDGES VERTICES_IN_INEQUALITIES
F2_VECTOR N_SITES VIF_CYCLIC_NORMAL
FACETS N_VERTEX_FACET_INC VOLUME
FACETS_THRU_VERTICES N_VERTICES VORONOI_GRAPH
FACET_DEGREES POINTED VORONOI_VERTICES
FACET_LABELS POINTS ZONOTOPE_INPUT_VECTORS
methods:
CD_INDEX VISUAL VISUAL_GRAPH
DUAL_FACE_LATTICE VISUAL_BOUNDED_GRAPH VISUAL_TRIANGULATION
FACE_LATTICE VISUAL_DUAL VISUAL_TRIANGULATION_BOUNDARY
GALE VISUAL_DUAL_FACE_LATTICE VISUAL_VORONOI
N_FLAGS VISUAL_DUAL_GRAPH makeSchlegelDiagram
SCHLEGEL VISUAL_FACE_LATTICE makeSchlegelSteinerPoints

RationalPolytope
A polyhedron realized in Qd
derived from:
Polytope
properties:
ABSTRACT_OBJECTIVE FACET_SIZES POINTS_IN_FACETS
AFFINE_HULL FACE_SIMPLICITY POSITIVE
ALTSHULER_DET FAR_FACE RANDOM_EDGE_EPL
AMBIENT_DIM FAR_HYPERPLANE REL_INT_POINT
BALANCE FATNESS REVERSE_TRANSFORMATION
BALANCED FEASIBLE SCHLEGEL_PARAMS
BOUNDED FLAG_VECTOR SIMPLE
BOUNDED_GRAPH FTV_CYCLIC_NORMAL SIMPLICIAL
BOUNDING_BOX F_VECTOR SIMPLICIALITY
CD_INDEX_COEFFICIENTS GALE_TRANSFORM SIMPLICITY
CENTERED GALE_VERTICES SITES
CHIROTOPE GRAPH SITE_LABELS
CHIROTOPE_INT HASSE_DIAGRAM STEINER_POINTS
COCUBICAL H_VECTOR TRIANGLE_FREE
COCUBICALITY INEQUALITIES TRIANGULATION
COMPLEXITY ITERATED_DELAUNAY_GRAPH TRIANGULATION_BOUNDARY
CONNECTIVITY ITERATED_VORONOI_GRAPH TRIANGULATION_INT
CRUST_GRAPH LINEAR_OBJECTIVE TRIANGULATION_INT_SIGNS
CUBICAL MAXIMAL_FACE TRIANGULATION_SIGNS
CUBICALITY MAXIMAL_VALUE UNBOUNDED_FACETS
CUBICAL_H_VECTOR MAXIMAL_VERTEX VALID_POINT
DELAUNAY_GRAPH MINIMAL_FACE VARIABLE_NAMES
DIAMETER MINIMAL_VALUE VERTEX_BARYCENTER
DIM MINIMAL_VERTEX VERTEX_COLORS
DIRECTED_GRAPH NEIGHBORLINESS VERTEX_DEGREES
DUAL_CONNECTIVITY NEIGHBORLY VERTEX_IN_DEGREES
DUAL_DIAMETER NEIGHBOR_FACETS_CYCLIC_NORMAL VERTEX_LABELS
DUAL_EVEN NEIGHBOR_VERTICES_CYCLIC_NORMAL VERTEX_NORMALS
DUAL_GRAPH N_BOUNDED_VERTICES VERTEX_OUT_DEGREES
DUAL_TRIANGLE_FREE N_EDGES VERTEX_SIZES
EQUATIONS N_FACETS VERTICES
ESSENTIALLY_GENERIC N_POINTS VERTICES_IN_FACETS
EVEN N_RIDGES VERTICES_IN_INEQUALITIES
F2_VECTOR N_SITES VIF_CYCLIC_NORMAL
FACETS N_VERTEX_FACET_INC VOLUME
FACETS_THRU_VERTICES N_VERTICES VORONOI_GRAPH
FACET_DEGREES POINTED VORONOI_VERTICES
FACET_LABELS POINTS ZONOTOPE_INPUT_VECTORS
methods:
CD_INDEX VISUAL VISUAL_GRAPH
DUAL_FACE_LATTICE VISUAL_BOUNDED_GRAPH VISUAL_TRIANGULATION
FACE_LATTICE VISUAL_DUAL VISUAL_TRIANGULATION_BOUNDARY
GALE VISUAL_DUAL_FACE_LATTICE VISUAL_VORONOI
N_FLAGS VISUAL_DUAL_GRAPH makeSchlegelDiagram
SCHLEGEL VISUAL_FACE_LATTICE makeSchlegelSteinerPoints

FloatPolytope
A polyhedron realized in R^d.
Convex hull and related algorithms use floating-point arithmetics. Due to numerical errors inherent to this kind of computations, the resulting combinatorial description can be arbitrarily far away from the truth, or even not correspond to any valid polytope. You have been warned.
None of the standard construction clients produces objects of this type. If you want to get one, create it with the explicit constructor or "re-bless" an existing RationalPolytope object; the coordinates stored in it don't need to be converted.
derived from:
Polytope
properties:
ABSTRACT_OBJECTIVE FACET_SIZES POSITIVE
AFFINE_HULL FACE_SIMPLICITY RANDOM_EDGE_EPL
ALTSHULER_DET FAR_FACE REL_INT_POINT
AMBIENT_DIM FAR_HYPERPLANE REVERSE_TRANSFORMATION
BALANCE FATNESS SCHLEGEL_PARAMS
BALANCED FEASIBLE SIMPLE
BOUNDED FLAG_VECTOR SIMPLICIAL
BOUNDED_GRAPH FTV_CYCLIC_NORMAL SIMPLICIALITY
BOUNDING_BOX F_VECTOR SIMPLICITY
CD_INDEX_COEFFICIENTS GALE_TRANSFORM SITES
CENTERED GALE_VERTICES SITE_LABELS
CHIROTOPE GRAPH STEINER_POINTS
CHIROTOPE_INT HASSE_DIAGRAM TRIANGLE_FREE
COCUBICAL H_VECTOR TRIANGULATION
COCUBICALITY INEQUALITIES TRIANGULATION_BOUNDARY
COMPLEXITY ITERATED_DELAUNAY_GRAPH TRIANGULATION_INT
CONNECTIVITY ITERATED_VORONOI_GRAPH TRIANGULATION_INT_SIGNS
CRUST_GRAPH LINEAR_OBJECTIVE TRIANGULATION_SIGNS
CUBICAL MAXIMAL_FACE UNBOUNDED_FACETS
CUBICALITY MAXIMAL_VALUE VALID_POINT
CUBICAL_H_VECTOR MAXIMAL_VERTEX VARIABLE_NAMES
DELAUNAY_GRAPH MINIMAL_FACE VERTEX_BARYCENTER
DIAMETER MINIMAL_VALUE VERTEX_COLORS
DIM MINIMAL_VERTEX VERTEX_DEGREES
DIRECTED_GRAPH NEIGHBORLINESS VERTEX_IN_DEGREES
DUAL_CONNECTIVITY NEIGHBORLY VERTEX_LABELS
DUAL_DIAMETER NEIGHBOR_FACETS_CYCLIC_NORMAL VERTEX_NORMALS
DUAL_EVEN NEIGHBOR_VERTICES_CYCLIC_NORMAL VERTEX_OUT_DEGREES
DUAL_GRAPH N_BOUNDED_VERTICES VERTEX_SIZES
DUAL_TRIANGLE_FREE N_EDGES VERTICES
EPSILON N_FACETS VERTICES_IN_FACETS
EQUATIONS N_POINTS VERTICES_IN_INEQUALITIES
ESSENTIALLY_GENERIC N_RIDGES VIF_CYCLIC_NORMAL
EVEN N_SITES VOLUME
F2_VECTOR N_VERTEX_FACET_INC VORONOI_GRAPH
FACETS N_VERTICES VORONOI_VERTICES
FACETS_THRU_VERTICES POINTED ZONOTOPE_INPUT_VECTORS
FACET_DEGREES POINTS
FACET_LABELS POINTS_IN_FACETS
methods:
CD_INDEX VISUAL VISUAL_GRAPH
DUAL_FACE_LATTICE VISUAL_BOUNDED_GRAPH VISUAL_TRIANGULATION
FACE_LATTICE VISUAL_DUAL VISUAL_TRIANGULATION_BOUNDARY
GALE VISUAL_DUAL_FACE_LATTICE VISUAL_VORONOI
N_FLAGS VISUAL_DUAL_GRAPH makeSchlegelDiagram
SCHLEGEL VISUAL_FACE_LATTICE makeSchlegelSteinerPoints

SchlegelDiagram
A Schlegel diagram of a polytope
properties:
FACET Polytope ZOOM
FACET_POINT TRANSFORM
INNER_POINT VERTICES
methods:
VISUAL

TightSpan
Bounded subcomplex of an unbounded polyhedron, which is associated with a finite metric space. The tight span is 1-dimensional if and only if the metric is tree-like. In this sense, the tight span captures the deviation of the metric from a tree-like one.
derived from:
RationalPolytope
properties:
ABSTRACT_OBJECTIVE FACE_SIMPLICITY POINTS_IN_FACETS
AFFINE_HULL FAR_FACE POSITIVE
ALTSHULER_DET FAR_HYPERPLANE RANDOM_EDGE_EPL
AMBIENT_DIM FATNESS REL_INT_POINT
BALANCE FEASIBLE REVERSE_TRANSFORMATION
BALANCED FLAG_VECTOR SCHLEGEL_PARAMS
BOUNDED FTV_CYCLIC_NORMAL SIMPLE
BOUNDED_GRAPH F_VECTOR SIMPLICIAL
BOUNDING_BOX GALE_TRANSFORM SIMPLICIALITY
CD_INDEX_COEFFICIENTS GALE_VERTICES SIMPLICITY
CENTERED GRAPH SITES
CHIROTOPE HASSE_DIAGRAM SITE_LABELS
CHIROTOPE_INT H_VECTOR STEINER_POINTS
COCUBICAL INEQUALITIES TAXA
COCUBICALITY ITERATED_DELAUNAY_GRAPH TRIANGLE_FREE
COMPLEXITY ITERATED_VORONOI_GRAPH TRIANGULATION
CONNECTIVITY LINEAR_OBJECTIVE TRIANGULATION_BOUNDARY
CRUST_GRAPH MAXIMAL_FACE TRIANGULATION_INT
CUBICAL MAXIMAL_VALUE TRIANGULATION_INT_SIGNS
CUBICALITY MAXIMAL_VERTEX TRIANGULATION_SIGNS
CUBICAL_H_VECTOR METRIC UNBOUNDED_FACETS
DELAUNAY_GRAPH MINIMAL_FACE VALID_POINT
DIAMETER MINIMAL_VALUE VARIABLE_NAMES
DIM MINIMAL_VERTEX VERTEX_BARYCENTER
DIRECTED_GRAPH NEIGHBORLINESS VERTEX_COLORS
DUAL_CONNECTIVITY NEIGHBORLY VERTEX_DEGREES
DUAL_DIAMETER NEIGHBOR_FACETS_CYCLIC_NORMAL VERTEX_IN_DEGREES
DUAL_EVEN NEIGHBOR_VERTICES_CYCLIC_NORMAL VERTEX_LABELS
DUAL_GRAPH NODE_COLORS VERTEX_NORMALS
DUAL_TRIANGLE_FREE N_BOUNDED_VERTICES VERTEX_OUT_DEGREES
EQUATIONS N_EDGES VERTEX_SIZES
ESSENTIALLY_GENERIC N_FACETS VERTICES
EVEN N_POINTS VERTICES_IN_FACETS
F2_VECTOR N_RIDGES VERTICES_IN_INEQUALITIES
FACETS N_SITES VIF_CYCLIC_NORMAL
FACETS_THRU_VERTICES N_VERTEX_FACET_INC VOLUME
FACET_DEGREES N_VERTICES VORONOI_GRAPH
FACET_LABELS POINTED VORONOI_VERTICES
FACET_SIZES POINTS ZONOTOPE_INPUT_VECTORS
methods:
CD_INDEX VISUAL_BOUNDED_GRAPH VISUAL_TIGHT_SPAN
DUAL_FACE_LATTICE VISUAL_DUAL VISUAL_TRIANGULATION
FACE_LATTICE VISUAL_DUAL_FACE_LATTICE VISUAL_TRIANGULATION_BOUNDARY
GALE VISUAL_DUAL_GRAPH VISUAL_VORONOI
N_FLAGS VISUAL_FACE_LATTICE makeSchlegelDiagram
SCHLEGEL VISUAL_GRAPH makeSchlegelSteinerPoints
VISUAL VISUAL_SPLITS