# Truncated tetrahedral prism

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Truncated tetrahedral prism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Tuttip |

Coxeter diagram | x x3x3o () |

Elements | |

Cells | 4 triangular prisms, 4 hexagonal prisms, 2 truncated tetrahedra |

Faces | 8 triangles, 6+12 squares, 8 hexagons |

Edges | 12+12+24 |

Vertices | 24 |

Vertex figure | Sphenoid, edge lengths 1, √3, √3 (base), √2 (legs) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Trip–4–hip: |

Tut–6–hip: 90° | |

Tut–3–trip: 90° | |

Hip–4–hip: | |

Height | 1 |

Central density | 1 |

Number of pieces | 10 |

Level of complexity | 12 |

Related polytopes | |

Army | Tuttip |

Regiment | Tuttip |

Dual | Triakis tetrahedral tegum |

Conjugate | None |

Abstract properties | |

Flag count | 576 |

Euler characteristic | 0 |

Topological properties | |

Orientable | Yes |

Properties | |

Symmetry | A_{3}×A_{1}, order 48 |

Convex | Yes |

Nature | Tame |

Discovered by | {{{discoverer}}} |

The **truncated tetrahedral prism** or **tuttip** is a prismatic uniform polychoron that consists of 2 truncated tetrahedra, 4 hexagonal prisms, and 4 triangular prisms. Each vertex joins 1 truncated tetrahedron, 1 triangular prism, and 2 hexagonal prisms. As the name suggests, it is a prism based on the truncated tetrahedron. As such it is also a convex segmentochoron (designated K-4.57 on Richard Klitzing's list).

## Gallery[edit | edit source]

Card with cell counts, verf, and cross-sections

Segmentochoron display, tut atop tut

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a truncated tetrahedral prism of edge length 1 are given by all permutations and even sign changes of the first three coordinates of:

## Representations[edit | edit source]

A truncated tetrahedral prism has the following Coxeter diagrams:

- x x3x3o (full symmetry)
- xx3xx3oo&#x (bases considered separately)
- x2s4o3x () (bases as snub)
- xxx xux3oox&#xt (A
_{2}×A_{1}symmetry, triangular prism-first) - x(xu)(xu)x-3-x(xo)(oo)o-&#xr (A
_{2}axial) - xxxx xuxo oxux&#xt (A
_{1}×A_{1}×A_{1}axial, square-first)

## External links[edit | edit source]

- Bowers, Jonathan. "Category 19: Prisms" (#898).

- Klitzing, Richard. "Tuttip".

- Wikipedia Contributors. "Truncated tetrahedral prism".