BUILT-IN MATHEMATICA SYMBOL

PolyhedronData

PolyhedronData[poly, "property"]
gives the value of the specified property for the polyhedron named poly.

PolyhedronData[poly]
gives an image of the polyhedron named poly.

PolyhedronData["class"]
gives a list of the polyhedra in the specified class.

DetailsDetails

• Polyhedra can be specified by standard names such as and .
• Classes of polyhedra supported include , , , , , and .
• or gives a list of all available polyhedra.
• PolyhedronData[patt] gives a list of all polyhedron names that match the string pattern patt.
• gives a list of polyhedra with n faces, with faces not necessarily being convex.
• PolyhedronData[;;n] gives a list of polyhedra with ≤ n faces.
• PolyhedronData[m;;n] gives a list of all standard polyhedra with m through n faces.
• PolyhedronData["class", n], etc. gives a list of polyhedra in the specified class with n faces, etc.
• PolyhedronData["Classes"] gives a list of all supported classes.
• PolyhedronData["Properties"] gives a list of properties available for polyhedra.
• For coordinate purposes, all polyhedra are taken to have smallest edges of unit length.
• Basic graphics-related properties include:
•  "Edges" graphics primitives for edges in the polyhedron "Faces" graphics primitives for faces of the polyhedron "Image" complete image of the polyhedron
• Combinatorial properties include:
•  "AdjacentFaceIndices" lists of indices for adjacent pairs of faces "EdgeCount" total number of edges "EdgeIndices" indices specifying the vertices on each edge "FaceCount" total number of faces "FaceCountRules" rules for the numbers of n-sided faces "FaceIndices" lists of indices for the vertices of each face "VertexCount" total number of vertices
• Coordinate-related properties include:
•  "Centroid" coordinates of the centroid in the standard embedding "InertiaTensor" inertia tensor of the solid polyhedron assuming unit mass "RegionFunction" pure function giving True in the interior of the polyhedron "VertexCoordinates" coordinates of vertices assuming unit smallest edge length
• Geometrical properties include:
•  "Circumcenter" center of circumscribed sphere "Circumradius" circumradius assuming unit smallest edge length "Circumsphere" graphics primitive for the circumscribed sphere "DihedralAngleRules" rules for dihedral angles "EdgeLengths" relative lengths of edges "GeneralizedDiameter" maximum distance between a pair of vertices "Incenter" center of inscribed sphere "Inradius" inradius assuming unit smallest edge length "Insphere" inscribed sphere "Midcenter" center of reciprocating sphere "Midradius" midradius assuming unit smallest edge length "Midsphere" graphics primitive for the reciprocating sphere "SurfaceArea" total surface area assuming unit smallest edge length "VertexSubsetHulls" rules for vertices whose hulls form other solids "Volume" enclosed volume assuming unit smallest edge length
• Properties of polyhedron nets include:
•  "NetCoordinates" coordinates of vertices in the net "NetCount" number of topologically distinct nets that can be drawn "NetEdgeIndices" indices specifying the vertices on each edge in the net "NetEdges" graphics primitives for edges in the net "NetFaceIndices" indices specifying the incidence of faces in the net "NetFaces" graphics primitives for faces in the net "NetGraph" net as a Graph object "NetImage" image of the polyhedron net
• Properties of polyhedron skeleton graphs include:
•  "SkeletonCoordinates" vertex positions in an embedding of the skeleton graph "SkeletonGraph" skeleton graph as a Graph object "SkeletonGraphName" name of the corresponding GraphData object "SkeletonImage" image of the skeleton graph "SkeletonRules" rules specifying the connectivity of the skeleton graph
• Overall properties include:
•  "Classes" classes of which the polyhedron is a member "DualName" name of the dual of the polyhedron "NotationRules" formal notations for the polyhedron "SymmetryGroupString" name of the symmetry group for the polyhedron
• PolyhedronData[name, "class"] gives True if the polyhedron is in the specified class.
• Classes of polyhedra include:
•  "Amphichiral" amphichiral solid "Chiral" chiral solid "Compound" compound of two or more polyhedra "Concave" concave solid "Convex" convex solid "Deltahedron" solid consisting of congruent equilateral triangles "Equilateral" all sides have unit length "Isohedron" symmetries act transitively on polyhedron faces "SelfDual" polyhedron is its own dual "SpaceFilling" space-filling polyhedron "Stellation" stellation of a polyhedron "Zonohedron" zonohedron
• Classes of polyhedra that are members of finite families include:
•  "Archimedean" one of the 13 Archimedean solids "ArchimedeanDual" one of the 13 Archimedean duals "Johnson" one of the 92 Johnson solids "KeplerPoinsot" one of the four Kepler-Poinsot solids "Platonic" one of the five Platonic solids "PlatonicDual" one of the five Platonic duals "Uniform" one of the 80 uniform polyhedra "UniformDual" one of the 80 uniform duals
• Classes of polyhedra indexed by an integer include:
•  "Antiprism" antiprism "Dipyramid" dipyramid "Prism" prism "Pyramid" pyramid
• Naming-related properties include:
•  "AlternateNames" alternate English names, as strings "AlternateStandardNames" alternate standard Mathematica names "Name" English name as a string "StandardName" standard Mathematica name
• PolyhedronData[name, "property", "ann"] or PolyhedronData["property", "ann"] gives various annotations associated with a property. Typical annotations include:
•  "Description" short textual description of the property "Information" hyperlink to additional information "LongDescription" longer textual description of the property "Value" the value of the property
• Using PolyhedronData may require internet connectivity.

ExamplesExamplesopen allclose all

Basic Examples (6)Basic Examples (6)

Show an image of a dodecahedron:

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Show the net of a dodecahedron:

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Show the snub cube with colored faces and transparency with no external lighting:

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Show the snub cube with colored faces and transparency in the presence of external lighting:

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Count the number of edges of an icosahedron:

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Vertex coordinates for a unit tetrahedron:

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A list of Archimedean polyhedra:

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