# Truncated cuboctahedral prism

Truncated cuboctahedral prism | |
---|---|

Schlegel diagram | |

Type | Prismatic uniform polychoron |

Uniform index | 55 |

Schläfli symbol | t_{0,1,2,3}{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 | 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.

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.

Vertex figure for full snub cuboctahedral antiprism

## External links

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