Truncated icosidodecahedral prism

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

Truncated icosidodecahedral prism
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
Cells	64 total: 2 4.6.10 30 4.4.4 20 4.4.6 12 4.4.10
Faces	304 total: 240 {4} 40 {6} 24 {5}
Edges	480
Vertices	240
Vertex figure	Irregular tetrahedron
Symmetry group	[5,3,2], order 240
Properties	convex

Net

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

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

Related polytopes

A full snub dodecahedral antiprism or omnisnub dodecahedral antiprism can be defined as an alternation of an truncated icosidodecahedral prism, represented by ht_0,1,2,3{5,3,2}, or , 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, 480 edges, and 544 faces (24 pentagons and 40+480 triangles). It has [5,3,2]⁺ symmetry, order 120.

Vertex figure for the omnisnub dodecahedral antiprism

External links

• 6. Convex uniform prismatic polychora - Model 63, George Olshevsky.
• Klitzing, Richard. "4D uniform polytopes (polychora) x x3o5x - griddip".