# Truncated cubic prism

Truncated cubic prism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Ticcup |

Coxeter diagram | x x4x3o () |

Elements | |

Cells | 8 triangular prisms, 6 octagonal prisms, 2 truncated cubes |

Faces | 16 triangles, 12+24 squares, 12 octagons |

Edges | 24+24+48 |

Vertices | 48 |

Vertex figure | Sphenoid, edge lengths 1, √2+√2, √2+√2 (base), √2 (legs) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Trip–4–op: |

Op–4–op: 90° | |

Tic–8–op: 90° | |

Tic–3–trip: 90° | |

Height | 1 |

Central density | 1 |

Number of pieces | 16 |

Level of complexity | 12 |

Related polytopes | |

Army | Ticcup |

Regiment | Ticcup |

Dual | Triakis octahedral tegum |

Conjugate | Quasitruncated hexahedral prism |

Abstract properties | |

Flag count | 1152 |

Euler characteristic | 0 |

Topological properties | |

Orientable | Yes |

Properties | |

Symmetry | B_{3}×A_{1}, order 96 |

Convex | Yes |

Nature | Tame |

Discovered by | {{{discoverer}}} |

The **truncated cubic prism** or **ticcup**, is a prismatic uniform polychoron that consists of 2 truncated cubes, 6 octagonal prisms, and 8 triangular prisms. Each vertex joins 1 truncated cube, 1 octagonal prism, and 2 triangular prisms. As the name suggests, it is a prism based on the truncated cube. As such it is also a convex segmentochoron (designated K-4.99 on Richard Klitzing's list).

The truncated cubic prism can be obtained from a small rhombated tesseract by removing two small rhombicuboctahedron atop truncated cube segmentochora. This diminishing cuts the lateral small rhombicuboctahedra into their equatorial octagonal prisms only. It is also a central segment of the small prismatotetracontoctachoron.

## Gallery[edit | edit source]

Card with cell counts, verf, and cross-sections

Segmentochoron display, tic atop tic

## Vertex coordinates[edit | edit source]

The vertices of a truncated cubic prism of edge length 1 are given by all permutations of the first three coordinates of:

## Representations[edit | edit source]

The truncated cubic prism has the following Coxeter diagrams:

- x x4x3o (full symmetry)
- xx4xx3oo&#x (bases considered separately)
- xxxx xwwx4xoox&#xt (BC
_{2}×A_{1}axial, octagonal prism-first)

## External links[edit | edit source]

- Bowers, Jonathan. "Category 19: Prisms" (#899).

- Klitzing, Richard. "Ticcup".

- Wikipedia Contributors. "Truncated cubic prism".