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

  • EntityClass["Polyhedron","Icosahedron"]

Properties

  • AdjacentFaceIndicesadjacent face indices
    AlternateNamesalternate names
    Amphichiralamphichiral
    Antiprismantiprism
    ArchimedeanArchimedean
    ArchimedeanDualArchimedean dual
    AssociatedPeopleassociated people
    BoundaryMeshRegionboundary mesh representation
    Centroidcentroid
    Chiralchiral
    Circumcentercircumcenter
    Circumdiametercircumdiameter
    Circumradiuscircumradius
    Circumspherecircumsphere
    Classesclasses
    Compoundcompound
    Concaveconcave
    Convexconvex
    Deltahedrondeltahedron
    DihedralAngleRulesdihedral angle rules
    DihedralAnglesdihedral angles
    Dipyramiddipyramid
    Dualdual
    EdgeCountedge count
    EdgeIndicesedge indices
    EdgeLengthsedge lengths
    Edgesedges
    EntityClassesentity classes
    Equilateralequilateral
    EulerCharacteristicEuler characteristic
    FaceCountface count
    FaceCount10decagonal face count
    FaceCount11hendecagonal face count
    FaceCount12dodecagonal face count
    FaceCount3triangular face count
    FaceCount4tetragonal face count
    FaceCount5pentagonal face count
    FaceCount6hexagonal face count
    FaceCount7heptagonal face count
    FaceCount8octagonal face count
    FaceCount9nonagonal face count
    FaceCountRulesface types
    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
    Namename
    NetCoordinatesnet coordinates
    NetCountnet count
    NetEdgeIndicesnet edge indices
    NetEdgesnet edges
    NetFaceIndicesnet face indices
    NetFacesnet faces
    NetGraphnet graph
    NetImagenet image
    NotationRulesnotation rules
    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
    SkeletonGraphskeleton graph
    SpaceFillingspacefilling polyhedron
    Stellationstellation
    StellationCountstellation count
    SurfaceAreasurface area
    SymmetryGroupsymmetry group
    Uniformuniform solid
    UniformDualuniform solid dual
    VertexCoordinatesvertex coordinates
    VertexCountvertex count
    VertexIndicesvertex indices
    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]:
  • "Source"source information for the property
    "Date"the date associated with the entity-property value (if any)
    "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]:
  • "Qualifiers"the list of possible qualifiers for the property
    "QualifierValues"the list of possible values that can be given to each qualifier
    "DefaultQualifierValues"the list of default values for the property's qualifiers
    "Description"a brief textual description of the property
    "Definition"a detailed textual definition of the property
    "PhysicalQuantity"the physical quantity associated with the entity-property value
    "Unit"the unit associated with the entity-property value
  • A qualifier value of Automatic indicates that an applicable format of values can be used; e.g. for the "Date" qualifier, this includes a proper date or date span.

Examples

Basic Examples  (4)

Use for entity discovery:

In[1]:=
Click for copyable input
Out[1]=

Find a property value for an entity:

In[1]:=
Click for copyable input
Out[1]=

Retrieve a dataset of all available properties for an entity:

In[1]:=
Click for copyable input
Out[1]=

Return the polyhedra associated with Albrecht Dürer:

In[1]:=
Click for copyable input
Out[1]=