Truncated icosidodecahedral prism

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Truncated icosidodecahedral prism
Truncated icosidodecahedral prism.png
Schlegel diagram
Type Prismatic uniform 4-polytope
Uniform index 63
Schläfli symbol t0,1,2,3{3,5,2} or tr{3,5}×{}
Coxeter-Dynkin CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 5.pngCDel node 1.pngCDel 2.pngCDel node 1.png
Cells 64 total:

2 Great rhombicosidodecahedron.png 4.6.10
30 Hexahedron.png 4.4.4
20 Hexagonal prism.png 4.4.6
12 Decagonal prism.png 4.4.10

Faces 304 total:
240 {4}
40 {6}
24 {5}
Edges 480
Vertices 240
Vertex figure Truncated icosidodecahedral prism verf.png
Isosceles-triangular pyramid
Symmetry group [5,3,2], order 240
Properties convex

In geometry, a truncated icosidodecahedral prism or great rhombicosidodecahedral prism is a convex uniform 4-polytope (four-dimensional polytope).

It is one of 18 convex uniform polyhedral prisms created by using uniform prisms to connect pairs of Platonic solids or Archimedean solids in parallel hyperplanes.

Alternative names[edit]

  • Truncated icosidodecahedral dyadic prism (Norman W. Johnson)
  • Griddip (Jonathan Bowers: for great rhombicosidodecahedral prism/hyperprism)
  • Great rhombicosidodecahedral prism/hyperprism

Related polytopes[edit]

A full snub dodecahedral antiprism or omnisnub dodecahedral antiprism can be defined as an alternation of an truncated icosidodecahedral prism, represented by ht0,1,2,3{5,3,2}, or CDel node h.pngCDel 5.pngCDel node h.pngCDel 3.pngCDel node h.pngCDel 2x.pngCDel node h.png, although it cannot be constructed as a uniform 4-polytope. It has 184 cells: 2 snub dodecahedrons connected by 30 tetrahedrons, 12 pentagonal antiprisms, and 20 octahedrons, with 120 tetrahedrons in the alternated gaps. It has 120 vertices, 220 edges, and 284 faces (24 pentagons, and 260 triangles). It has [5,3,2]+ symmetry, order 120.

Snub 532 verf.png
Vertex figure for full snub dodecahedral antiprism

External links[edit]