Truncated cuboctahedral prism

Truncated cuboctahedral prism
Schlegel diagram
Type	Prismatic uniform polychoron
Uniform index	55
Schläfli symbol	t0,1,2,3{4,3,2} or tr{4,3}×{}
Coxeter-Dynkin
Cells	28 total: 2 4.6.8 12 4.4.4 8 4.4.6 6 4.4.8
Faces	124 total: 96 {4} 16 {6} 12 {8}
Edges	192
Vertices	96
Vertex figure	80px irr. tetrahedron
Symmetry group	[4,3,2], order 96
Properties	convex

In geometry, a truncated cuboctahedral prism or great rhombicuboctahedral prism is a convex uniform polychoron (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.

320px
Net

Alternative names

• Truncated-cuboctahedral dyadic prism (Norman W. Johnson)
• Gircope (Jonathan Bowers: for great rhombicuboctahedral prism/hyperprism)
• Great rhombicuboctahedral prism/hyperprism

Related polytopes

A full snub cubic antiprism or omnisnub cubic antiprism can be defined as an alternation of an truncated cuboctahedral prism, represented by ht_0,1,2,3{4,3,2}, or , although it cannot be constructed as a uniform polychoron. It has 76 cells: 2 snub cubes connected by 12 tetrahedrons, 6 square antiprisms, and 8 octahedrons, with 48 tetrahedrons in the alternated gaps. There are 48 vertices, 192 edges, and 220 faces (12 squares, and 16+192 triangles). It has [4,3,2]⁺ symmetry, order 48.

160px
Vertex figure for full snub cuboctahedral antiprism

External links

• 6. Convex uniform prismatic polychora - Model 55, George Olshevsky.
• Richard Klitzing, 4D uniform polytopes (polychora), x3x4x x - gircope