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.

Details

  • 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[] and PolyhedronData[All] give a list of all available polyhedra.
  • 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[;;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.
  • Structural properties include:
  • "Edges"polyhedron edges (as vertex index pairs)
    "Faces"polyhedron faces (as vertex index lists)
    "Vertices"polyhedron vertices (as a list of vertex coordinates)
  • Graphical properties include:
  • "DualCompound"dual compound
    "Graphics3D"3D graphics expression
    "GraphicsComplex"graphics complex expression
    "Image"image
    "Polyhedron"rendered graphical representation of the polyhedron faces
  • Combinatorial properties include:
  • "EdgeCount"total number of edges
    "FaceCount"total number of faces
    "NetCount"number of topologically distinct nets that can be drawn
    "VertexCount"total number of vertices
  • PolyhedronData[name,"property","outputtype"] gives polyhedron properties in the format specified by "outputtype", which, depending on "property", may be "Adjacent", "Coordinates", "Count", "Entity", "Graph", "Graphics3D", "GraphicsComplex", "Group", "Image", "Length", "Line", "List", "Name", "Notation", "Point", "Polygon", "Polyhedron", "Rule", "Tally", or "Undirected".
  • Annotations related to polyhedron output and display include:
  • "DihedralAngles","outputtype"dihedral angles as a list of angles or set of rules indexed by adjacent face indices
    "Dual","outputtype"polyhedron dual as an entity standard name, entity, graphic, graphics complex, polyhedron, or scale
    "DualCompound","outputtype"polyhedron dual compound as a graphic, graphics complex, image, entity standard name, or entity
    "Edges","outputtype"edges as an indexed list, count, list of unique lengths, rule list, lines, graphic, graphics complex, or image
    "Faces","outputtype"faces as an indexed list, count, list of adjacent face indices, rule list of edge count tallies, polygons, graphic, graphics complex, or image
    "Net","outputtype"polyhedron net as a graphic, graphics compex, image, list of vertex coordinates, count, list of face indices, or graph
    "Skeleton","outputtype"skeleton graph as a graph, vertex coordinate list, image, graph entity standard name, graph entity, edge rule list, or undirected edge list
    "SymmetryGroup","outputtype"symmetry group as a group standard name, or entity
    "Vertices","outputtype"vertices as indices, count, point, graphics, graphics complex, or image
  • Region-related properties include:
  • "BoundaryMeshRegion"boundary mesh representation
    "ImplicitRegion"representation as inequalities and equalities
    "MeshRegion"mesh representation
    "Region"geometric region
    "RegionFunction"pure function giving True in the interior of the polyhedron
  • Geometrical properties include:
  • "Centroid"coordinates of the centroid in the standard embedding
    "Circumcenter"center of circumscribed sphere
    "Circumradius"circumradius assuming unit smallest edge length
    "Circumsphere"graphics primitive for the circumscribed sphere
    "DihedralAngles"dihedral angles
    "GeneralizedDiameter"maximum distance between a pair of vertices
    "Incenter"center of inscribed sphere
    "InertiaTensor"inertia tensor of the solid polyhedron assuming unit mass
    "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
  • Overall properties include:
  • "Classes"classes of which the polyhedron is a member
    "NotationRules"formal notations 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 4 Kepler-Poinsot solids
    "Platonic"one of the 5 Platonic solids
    "PlatonicDual"one of the 5 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 Wolfram Language names
    "Name"English name as a string
    "Entity"polyhedron entity
    "StandardName"standard Wolfram Language 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

Examples

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Basic Examples  (6)

Show a graphic of a dodecahedron:

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Show the net of a dodecahedron:

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Display as a graph:

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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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Scope  (142)

Generalizations & Extensions  (1)

Applications  (8)

Properties & Relations  (7)

Possible Issues  (6)

Neat Examples  (5)

See Also

SolidData  SpherePoints  Graphics3D  RegionPlot3D  Polygon  GraphData  "Polyhedron"  "PolyhedronClass"  "ComputedPolyhedron"

Introduced in 2007
(6.0)
| Updated in 2017
(11.1)