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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.
  • Polyhedra can be specified by standard names such as "Dodecahedron" and "TruncatedCube".
  • Classes of polyhedra supported include "Platonic", "Archimedean", "ArchimedeanDual", "KeplerPoinsot", "Johnson" and "Uniform".
  • PolyhedronData[patt] gives a list of all polyhedron names that match the string pattern patt.
  • PolyhedronData[n] gives a list of polyhedra with n faces, with faces not necessarily being convex.
  • 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
"RegionFunction"pure function giving True in the interior of the polyhedron
"VertexCoordinates"coordinates of vertices assuming unit smallest edge length
  • Geometrical properties include:
"Circumradius"circumradius assuming unit smallest edge length
"DihedralAngleRules"rules for dihedral angles
"EdgeLengths"relative lengths of edges
"GeneralizedDiameter"maximum distance between a pair of vertices
"Inradius"inradius assuming unit smallest edge length
"Midradius"midradius assuming unit smallest edge length
"SurfaceArea"total surface area assuming unit smallest edge length
"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
"NetImage"image of the polyhedron net
  • Properties of polyhedron skeleton graphs include:
"SkeletonCoordinates"vertex positions in an embedding of the skeleton graph
"SkeletonImage"image of the skeleton graph
"SkeletonRules"rules specifying the connectivity of the skeleton graph
  • Overall properties include:
"Dual"dual of the polyhedron
"Classes"classes of which the polyhedron is a member
"NotationRules"formal notations for the polyhedron
"SymmetryGroupString"name of the symmetry group for the polyhedron
  • Classes of polyhedra include:
"Chiral"chiral solid
"Convex"convex solid
"Deltahedron"solid consisting of equilateral triangles
"Equilateral"all sides have unit length
"Zonohedron"zonohedron
  • 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
"LongDescription"longer textual description of the property
"Note"additional information about the property
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