# Faceted rectified tesseract

(Redirected from Firt)

Faceted rectified tesseract | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Firt |

Coxeter diagram | x3x3o3o3/2*a () |

Elements | |

Cells | |

Faces | 64 triangles, 32 hexagons |

Edges | 96 |

Vertices | 32 |

Vertex figure | Triangular retroprism, edge lengths 1 (base) and √3 (sides) |

Edge figure | tet 3 tut 6 tut 6 tut 3 |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angle | Tet–3–tut: 60° Tut–6–tut: 60° |

Central density | 4 |

Number of external pieces | 368 |

Level of complexity | 23 |

Related polytopes | |

Army | Rit |

Regiment | Rit |

Conjugate | None |

Convex core | Hexadecachoron |

Abstract & topological properties | |

Flag count | 1536 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | B_{4}, order 384 |

Flag orbits | 4 |

Convex | No |

Nature | Tame |

The **faceted rectified tesseract**, or **firt**, is a nonconvex uniform polychoron that consists of 16 regular tetrahedra and 16 truncated tetrahedra. Two tetrahedra and six truncated tetrahedra join at each vertex.

## Cross-sections[edit | edit source]

## Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the rectified tesseract.

## External links[edit | edit source]

- Bowers, Jonathan. "Category 3: Triangular Rectates" (#43).

- Klitzing, Richard. "firt".