BUILT-IN MATHEMATICA SYMBOL
PolyhedronData
PolyhedronData[poly, "property"]
gives the value of the specified property for 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
and 
.
- Classes of polyhedra supported include
, 
, 
, 
, 
, and 
.
- PolyhedronData[] or PolyhedronData[All] gives 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.
- 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.
Show an image of a dodecahedron:
| Out[1]= |  |
Show the net of a dodecahedron:
| Out[1]= |  |
| Out[2]= |  |
Show the snub cube with colored faces and transparency with no external lighting:
| Out[1]= |  |
Show the snub cube with colored faces and transparency in the presence of external lighting:
| Out[2]= |  |
Count the number of edges of an icosahedron:
| Out[1]= |  |
Vertex coordinates for a unit tetrahedron:
| Out[1]= |  |
A list of Archimedean polyhedra:
| Out[1]= |  |
New in 6 | Last modified in 8
