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Class PolytopeS<T>

Represents a polytope in a way that takes advantage of symmetry. Obviously, this requires a representation of the symmetry group. The other components are a description of how the flags (tuples of vertex/edge/face...) within a single domain connect to each other under "change vertex/edge/..." operations, matrices describing how the symmetry group affects the physical representation of the polytope, and positions of each class of vertices. In this implementation the symmetry group and its physical effects are bundled.

Type parameters

  • T

Hierarchy

Index

Constructors

constructor

Properties

construction

construction: ConstructionNode<unknown>

dimensions

dimensions: number

flagClasses

flagClasses: FlagClass[]

Stores the interactions between flag classes.

Private identitySimplifier

identitySimplifier: FlagMap<T, Flag<T>>

spaceDimensions

spaceDimensions: number

symmetries

symmetries: ConcreteGroup<T>

The symmetry group of the polytope.

Readonly type

vertices

vertices: Point[]

Stores a set of vertices that generates the entire polytope.

Methods

circumradius

  • circumradius(): number

compareFlags

  • compareFlags(flag1: Flag<T>, flag2: Flag<T>): -1 | 0 | 1

equalFlags

  • equalFlags(flag1: Flag<T>, flag2: Flag<T>): boolean

Private extendSimplifier

getName

  • getName(): string

gravicenter

  • The gravicenter is the gravicenter of the original vertices, weighted by the inverse of the number of domains each vertex appears in, projected onto the intersection of the eigenspaces of the generators with eigenvalues 1.

    Returns Point

Private mergeSimplifiers

Private modifySimplifier

move

moveFlag

  • moveFlag(flag: Flag<T>, generator: number): Flag<T>
  • Apply an element-change operation to a flag.

    Parameters

    • flag: Flag<T>

      The flag to apply the operation.

    • generator: number

      The index of the element that is changed.

    Returns Flag<T>

scale

setConstruction

simplifierCosets

  • simplifierCosets(simplifier: FlagMap<T, Flag<T>>): number
  • Counts a simplifier's cosets. Not needed except for debugging.

    Parameters

    • simplifier: FlagMap<T, Flag<T>>

      The simplifier to perform the count.

    Returns number

    The number of cosets of the simplifier.

toPolytopeC

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