Truncated cuboctahedral prism

Truncated cuboctahedral prism

Schlegel diagram
TypePrismatic uniform polychoron
Uniform index55
Schläfli symbolt0,1,2,3{4,3,2} or tr{4,3}×{}
Cells28 total:
2 4.6.8
12 4.4.4
8 4.4.6
6 4.4.8
Faces124 total:
96 {4}
16 {6}
12 {8}
Vertex figure
irr. tetrahedron
Symmetry group[4,3,2], order 96

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.


Alternative names

Related polytopes

A full snub cubic antiprism or omnisnub cubic antiprism can be defined as an alternation of an truncated cuboctahedral prism, represented by ht0,1,2,3{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.

Vertex figure for full snub cuboctahedral antiprism

External links

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