Polyhedron
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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
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Sample Entity Classes
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Properties
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AlternateNames alternate names Amphichiral amphichiral Antiprism antiprism Archimedean Archimedean ArchimedeanDual Archimedean dual AssociatedPeople associated people BoundaryMeshRegion boundary mesh representation Canonical canonical Centroid centroid Chiral chiral Circumcenter circumcenter Circumdiameter circumdiameter Circumradius circumradius Circumsphere circumsphere Classes classes Compound compound CompoundInterior compound interior Concave concave Convex convex ConvexHull convex hull CoordinateBounds coordinate bounds DefaultOrientation default orientation DehnInvariant Dehn invariant Deltahedron deltahedron DihedralAngles dihedral angles Dipyramid dipyramid Dual dual EdgeCount edge count EdgeIndices edge indices EdgeLengths distinct edge lengths EntityClasses entity classes EntityTypeList entity type list Equilateral equilateral FaceCount face count FaceIndices face indices GeneralizedDiameter generalized diameter Goldberg Goldberg polyhedron Graphics3D 3‐D graphics GraphicsComplex graphics complex Hull hull Image image ImplicitRegion representation as inequalities and equalities Incenter incenter InertiaTensor inertia tensor Information information Inradius inradius Insphere insphere Isohedron isohedron Johnson Johnson solid KeplerPoinsot Kepler‐Poinsot solid Lines lines MeanCylindricalRadius mean cylindrical radius MeanInteriorLineSegmentLength mean interior line segment length MeanSphericalRadius mean spherical radius MeanSquareCylindricalRadius mean square cylindrical radius MeanSquareSphericalRadius mean square spherical radius Midcenter midcenter Midradius midradius Midsphere midsphere MultipieceNetCoordinates multipiece net coordinates MultipieceNetFaceIndices multipiece net face indices MultipieceNetImage multipiece net image Name name Names name and alternate names Net net NetCount net count NotationRules notation rules Orientations orientations Parallelohedron parallelohedron Platonic Platonic solid PlatonicDual Platonic dual Plesiohedron plesiohedron Points points Polygons polygons Polyhedra polyhedra Polyhedron polyhedron Prism prism Pyramid pyramid Quasiregular quasiregular Region region RegionFunction region function Rhombohedron rhombohedron Rigid rigid polyhedron SchlaefliSymbol Schläfli symbol SelfDual self‐dual polyhedron Shaky shaky polyhedron Simple simple Skeleton skeleton SpaceFilling space‐filling polyhedron StableFaceIndices stable face indices Stellation stellation StellationCount stellation count Stereohedron stereohedron SurfaceArea surface area SymmetryGroup symmetry group Trapezohedron trapezohedron Uniform uniform solid UniformDual uniform solid dual Unistable unistable UnstableFaceIndices unstable face indices VertexCoordinates vertex coordinates VertexCount vertex count VertexSubsetHulls vertex subset hulls Volume volume WythoffSymbol Wythoff symbol Zalgaller Zalgaller polyhedron Zonohedron zonohedron
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:
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"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]:
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"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]:
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"Definition" a detailed textual definition of the property
for entity discovery: