The application polytope defines the following object types:

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

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

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

SchlegelDiagram
A Schlegel diagram of a polytope
properties:
FACET Polytope VIEWPOINT
FACET_POINT TRANSFORM ZOOM
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 FATNESS POSITIVE
AFFINE_HULL FEASIBLE RANDOM_EDGE_EPL
ALTSHULER_DET FLAG_VECTOR REL_INT_POINT
AMBIENT_DIM FTV_CYCLIC_NORMAL REVERSE_TRANSFORMATION
BALANCE F_VECTOR SCHLEGEL_PARAMS
BALANCED GALE_TRANSFORM SELF_DUAL
BOUNDED GALE_VERTICES SIMPLE
BOUNDED_GRAPH GRAPH SIMPLICIAL
CD_INDEX_COEFFICIENTS GRAPH_SIGNATURE SIMPLICIALITY
CENTERED G_VECTOR SIMPLICITY
CHIROTOPE HASSE_DIAGRAM SITES
CHIROTOPE_INT H_VECTOR SITE_LABELS
COCUBICAL INEQUALITIES STEINER_POINTS
COCUBICALITY ITERATED_DELAUNAY_GRAPH SUBRIDGE_SIZES
COMPLEXITY ITERATED_VORONOI_GRAPH TAXA
CONNECTIVITY LATTICE TRIANGLE_FREE
CRUST_GRAPH LINEAR_OBJECTIVE TRIANGULATION
CUBICAL MAXIMAL_FACE TRIANGULATION_BOUNDARY
CUBICALITY MAXIMAL_VALUE TRIANGULATION_INT
CUBICAL_H_VECTOR MAXIMAL_VERTEX TRIANGULATION_INT_SIGNS
DELAUNAY_GRAPH METRIC TRIANGULATION_SIGNS
DIAMETER MINIMAL_FACE TWO_FACE_SIZES
DIM MINIMAL_VALUE UNBOUNDED_FACETS
DIRECTED_GRAPH MINIMAL_VERTEX VALID_POINT
DUAL_CONNECTIVITY MINIMAL_VERTEX_ANGLE VARIABLE_NAMES
DUAL_DIAMETER NEIGHBORLINESS VERTEX_BARYCENTER
DUAL_EVEN NEIGHBORLY VERTEX_COLORS
DUAL_GRAPH NEIGHBOR_FACETS_CYCLIC_NORMAL VERTEX_DEGREES
DUAL_GRAPH_SIGNATURE NEIGHBOR_VERTICES_CYCLIC_NORMAL VERTEX_IN_DEGREES
DUAL_TRIANGLE_FREE NODE_COLORS VERTEX_LABELS
EDGE_COLORED_BOUNDED_GRAPH N_BOUNDED_VERTICES VERTEX_NORMALS
EQUATIONS N_EDGES VERTEX_OUT_DEGREES
ESSENTIALLY_GENERIC N_FACETS VERTEX_SIZES
EVEN N_INEQUALITIES VERTICES
F2_VECTOR N_NON_NEG_INT VERTICES_IN_FACETS
FACETS N_POINTS VERTICES_IN_INEQUALITIES
FACETS_THRU_VERTICES N_RIDGES VERTICES_IN_METRIC
FACET_DEGREES N_SITES VIF_CYCLIC_NORMAL
FACET_LABELS N_VERTEX_FACET_INC VOLUME
FACET_SIZES N_VERTICES VORONOI_BOUNDING_BOX
FACE_SIMPLICITY POINTED VORONOI_GRAPH
FAR_FACE POINTS VORONOI_VERTICES
FAR_HYPERPLANE POINTS_IN_FACETS ZONOTOPE_INPUT_VECTORS
methods:
CD_INDEX VISUAL_BOUNDED_GRAPH VISUAL_SPLITS
DUAL_FACE_LATTICE VISUAL_DUAL VISUAL_TIGHT_SPAN
FACE_LATTICE VISUAL_DUAL_FACE_LATTICE VISUAL_TRIANGULATION_BOUNDARY
GALE VISUAL_DUAL_GRAPH VISUAL_VORONOI
N_FLAGS VISUAL_EDGE_COLORED_BOUNDED_GRAPH makeSchlegelDiagram
SCHLEGEL VISUAL_FACE_LATTICE makeSchlegelSteinerPoints
VISUAL VISUAL_GRAPH

PropagatedPolytope
Polytope propagation means to define a polytope inductively by assigning vectors to arcs of a directed graph. At each node of such a graph a polytope arises as the joint convex hull of the polytopes at the translated sources of the inward pointing arcs.
derived from:
RationalPolytope
properties:
ABSTRACT_OBJECTIVE FAR_HYPERPLANE POSITIVE
AFFINE_HULL FATNESS RANDOM_EDGE_EPL
ALTSHULER_DET FEASIBLE REL_INT_POINT
AMBIENT_DIM FLAG_VECTOR REVERSE_TRANSFORMATION
BALANCE FTV_CYCLIC_NORMAL SCHLEGEL_PARAMS
BALANCED F_VECTOR SELF_DUAL
BOUNDED GALE_TRANSFORM SIMPLE
BOUNDED_GRAPH GALE_VERTICES SIMPLICIAL
CD_INDEX_COEFFICIENTS GRAPH SIMPLICIALITY
CENTERED GRAPH_SIGNATURE SIMPLICITY
CHIROTOPE G_VECTOR SITES
CHIROTOPE_INT HASSE_DIAGRAM SITE_LABELS
COCUBICAL H_VECTOR STEINER_POINTS
COCUBICALITY INEQUALITIES SUBRIDGE_SIZES
COMPLEXITY ITERATED_DELAUNAY_GRAPH SUM_PRODUCT_GRAPH
CONNECTIVITY ITERATED_VORONOI_GRAPH TRIANGLE_FREE
CRUST_GRAPH LATTICE TRIANGULATION
CUBICAL LINEAR_OBJECTIVE TRIANGULATION_BOUNDARY
CUBICALITY MAXIMAL_FACE TRIANGULATION_INT
CUBICAL_H_VECTOR MAXIMAL_VALUE TRIANGULATION_INT_SIGNS
DELAUNAY_GRAPH MAXIMAL_VERTEX TRIANGULATION_SIGNS
DIAMETER MINIMAL_FACE TWO_FACE_SIZES
DIM MINIMAL_VALUE UNBOUNDED_FACETS
DIRECTED_GRAPH MINIMAL_VERTEX VALID_POINT
DUAL_CONNECTIVITY MINIMAL_VERTEX_ANGLE VARIABLE_NAMES
DUAL_DIAMETER NEIGHBORLINESS VERTEX_BARYCENTER
DUAL_EVEN NEIGHBORLY VERTEX_COLORS
DUAL_GRAPH NEIGHBOR_FACETS_CYCLIC_NORMAL VERTEX_DEGREES
DUAL_GRAPH_SIGNATURE NEIGHBOR_VERTICES_CYCLIC_NORMAL VERTEX_IN_DEGREES
DUAL_TRIANGLE_FREE N_BOUNDED_VERTICES VERTEX_LABELS
EDGE_COLORED_BOUNDED_GRAPH N_EDGES VERTEX_NORMALS
EQUATIONS N_FACETS VERTEX_OUT_DEGREES
ESSENTIALLY_GENERIC N_INEQUALITIES VERTEX_SIZES
EVEN N_NON_NEG_INT VERTICES
F2_VECTOR N_POINTS VERTICES_IN_FACETS
FACETS N_RIDGES VERTICES_IN_INEQUALITIES
FACETS_THRU_VERTICES N_SITES VIF_CYCLIC_NORMAL
FACET_DEGREES N_VERTEX_FACET_INC VOLUME
FACET_LABELS N_VERTICES VORONOI_BOUNDING_BOX
FACET_SIZES POINTED VORONOI_GRAPH
FACE_SIMPLICITY POINTS VORONOI_VERTICES
FAR_FACE POINTS_IN_FACETS ZONOTOPE_INPUT_VECTORS
methods:
CD_INDEX VISUAL VISUAL_GRAPH
DUAL_FACE_LATTICE VISUAL_BOUNDED_GRAPH VISUAL_TRIANGULATION_BOUNDARY
FACE_LATTICE VISUAL_DUAL VISUAL_VORONOI
GALE VISUAL_DUAL_FACE_LATTICE makeSchlegelDiagram
N_FLAGS VISUAL_DUAL_GRAPH makeSchlegelSteinerPoints
SCHLEGEL VISUAL_FACE_LATTICE

Framework
A bar and joint framework is a graph with a given embedding.
properties:
DIM FRAMEWORK NODE_LABELS
EMBEDDING GRAPH N_DEGREES_OF_FREEDOM
EXPANSIVE_MOTIONS INFINITESIMALLY_RIGID N_EDGES
EXPANSIVE_MOTION_CONE INFINITESIMAL_MOTIONS N_NODES
EXPANSIVE_MOTION_COORDINATES INFINITESIMAL_MOTION_COORDINATES RIGIDITY_MATRIX
EXPANSIVE_PATTERNS INFINITESIMAL_PATTERNS
EXPANSIVE_RIGID_COMPONENTS INFINITESIMAL_RIGID_COMPONENTS
methods:
VISUAL