UniformPolyhedron

UniformPolyhedron["name"]

gives the uniform polyhedron with the given name.

UniformPolyhedron[{n,m}]

gives the uniform polyhedron with n sides of each face and m faces meeting at each vertex point.

UniformPolyhedron[{r,θ,ϕ},]

rescales the uniform polyhedron by a factor r and rotates by an angle θ with respect to the z axis and angle ϕ with respect to the y axis.

UniformPolyhedron[{x,y,z},{r,θ,ϕ},]

centers the uniform polyhedron at {x,y,z}.

Details

  • UniformPolyhedron is also known as Platonic solid, Archimedean solid or regular star polyhedron.
  • UniformPolyhedron is typically used to generate base shapes for 3D modeling and as geometric regions.
  • UniformPolyhedron generates a Polyhedron centered at the origin with unit edge length.
  • Uniform polyhedrons can be specified with their standard names, Schläfli symbols {n,m} or Wenninger numbers, including:
  • {4,3}"Cube"
    {5,3}"Dodecahedron"
    {3,5}"Icosahedron"
    {3,4}"Octahedron"
    {3,3}"Tetrahedron"
  • {{5,2},5}"SmallStellatedDodecahedron"
    {{5,2},3}"GreatStellatedDodecahedron"
    {3,{5,2}}"GreatIcosahedron"
    {5,{5,2}}"GreatDodecahedron"

Examples

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Basic Examples  (2)

A dodecahedron:

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Get a list of uniform polyhedra:

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Scope  (9)

Properties & Relations  (4)

Possible Issues  (1)

Neat Examples  (2)

Introduced in 2019
(12.0)