Notable polyhedra and polyhedron compounds.

Entity["Polyhedron",name] or

represents an entity of type "Polyhedron".

[prop]

gives the value of a specified property.

[{propi,}]

gives the value of a list of properties.

EntityClass["Polyhedron",{propispeci,}]

represents a class of entities with values of propi defined by speci.

Sample Entities

Sample Entity Classes

Properties

  • AlternateNamesalternate names
    Amphichiralamphichiral
    Antiprismantiprism
    ArchimedeanArchimedean
    ArchimedeanDualArchimedean dual
    AssociatedPeopleassociated people
    BoundaryMeshRegionboundary mesh representation
    Centroidcentroid
    Chiralchiral
    Circumcentercircumcenter
    Circumdiametercircumdiameter
    Circumradiuscircumradius
    Circumspherecircumsphere
    Classesclasses
    Compoundcompound
    Concaveconcave
    Convexconvex
    DefaultOrientationdefault orientation
    Deltahedrondeltahedron
    DihedralAnglesdihedral angles
    Dipyramiddipyramid
    Dualdual
    DualCompounddual compound
    EdgeCountedge count
    EdgeIndicesedge indices
    EdgeLengthsedge lengths
    EntityClassesentity classes
    Equilateralequilateral
    FaceCountface count
    FaceIndicesface indices
    GeneralizedDiametergeneralized diameter
    Graphics3D3D graphics
    GraphicsComplexgraphics complex
    Imageimage
    ImplicitRegionrepresentation as inequalities and equalities
    Incenterincenter
    InertiaTensorinertia tensor
    Informationinformation
    Inradiusinradius
    Insphereinsphere
    Isohedronisohedron
    JohnsonJohnson solid
    KeplerPoinsotKeplerPoinsot solid
    Lineslines
    MeshRegionmesh representation
    Midcentermidcenter
    Midradiusmidradius
    Midspheremidsphere
    MultipieceNetCoordinatesmultipiece net coordinates
    MultipieceNetFaceIndicesmultipiece net face indices
    MultipieceNetImagemultipiece net image
    Namename
    Namesname and alternate names
    Netnet
    NetCountnet count
    NotationRulesnotation rules
    Orientationsorientations
    PlatonicPlatonic solid
    PlatonicDualPlatonic dual
    Pointspoints
    Polygonspolygons
    Polyhedronpolyhedron
    PolyhedronCompoundComponentspolyhedron compound components
    Prismprism
    Pyramidpyramid
    Quasiregularquasiregular
    Regionregion
    RegionFunctionregion function
    Rhombohedronrhombohedron
    Rigidrigid polyhedron
    SchlaefliSymbolSchläfli symbol
    SelfDualselfdual polyhedron
    Shakyshaky polyhedron
    Skeletonskeleton
    SpaceFillingspacefilling polyhedron
    Stellationstellation
    StellationCountstellation count
    SurfaceAreasurface area
    SymmetryGroupsymmetry group
    Uniformuniform solid
    UniformDualuniform solid dual
    VertexCoordinatesvertex coordinates
    VertexCountvertex count
    VertexSubsetHullsvertex subset hulls
    Volumevolume
    WythoffSymbolWythoff symbol
    Zonohedronzonohedron

Details

  • "Polyhedron" entities include common solids such as Platonic solids and prisms as well as other solids of interest.
  • "Polyhedron" entity classes include common mathematical types of polyhedra such as "Convex", "Equilateral" and "Platonic".
  • "Polyhedron" entities are normalized so that the smallest edge always has unit length. Mathematical properties are available for most "Polyhedron" entities that are either well known or straightforward to compute. Properties for some parametrized "Polyhedron" entities are available for symbolic parameters.
  • Some properties are available for the "Polyhedron" entity type as a whole and can be given using the form EntityValue["Polyhedron",property]. Such properties include:
  • "Properties"the list of available properties
    "PropertyCanonicalNames"the standard names of available properties
    "SampleEntities"a sample list of available entities (typically of length 10)
    "SampleEntityClasses"a sample list of available entity classes (typically of length 10)
    "EntityCount"number of entities available
    "Entities"the list of available entities
    "EntityCanonicalNames"the standard names of available entities
    "EntityClasses"the list of available entity classes
    "EntityClassCanonicalNames"the standard names of available entity classes
    "PropertyClasses"the list of available property classes
    "PropertyClassCanonicalNames"the standard names of available property classes
    "PropertyCount"number of properties available
  • The following annotations can be used in the third argument of EntityValue["Polyhedron",property,annotation]:
  • "EntityAssociation"an association of entities and entity-property values
    "PropertyAssociation"an association of properties and entity-property values
    "EntityPropertyAssociation"an association in which the specified entities are keys, and values are a nested association of properties and entity-property values
    "PropertyEntityAssociation"an association in which the specified properties are keys, and values are a nested association of entities and entity-property values
    "Dataset"a dataset in which the specified entities are keys, and values are an association of property names and entity-property values
  • The following annotations can be used in the second argument of EntityValue[property,annotation]:
  • "Definition"a detailed textual definition of the property

Examples

Basic Examples  (4)

Use for entity discovery:

Find a property value for an entity:

Retrieve a dataset of all available properties for an entity:

Return the polyhedra associated with Albrecht Dürer:

Introduced in 2019
 (12.0)
 |
Updated in 2020
 (12.1)