# Small rhombated demitesseract

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Small rhombated demitesseract | |
---|---|

Rank | 4 |

Type | Semi-uniform |

Notation | |

Coxeter diagram | x3o3o *b3y |

Elements | |

Cells | 8+8 tetrahedra, 8 rhombitetratetrahedra |

Faces | 32+32 triangles, 24 rectangles |

Edges | 48+48 |

Vertices | 32 |

Vertex figure | Triangular frustum |

Measures (edge lengths a, b) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Ratet–3–tet: 120° |

Ratet–4–ratet: 90° | |

Central density | 1 |

Related polytopes | |

Dual | Triangular-tegmatic triacontadichoron |

Conjugate | Small rhombated demitesseract |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | D4, order 192 |

Convex | Yes |

Nature | Tame |

The **small rhombated demitesseract** or **runcic tesseract** is a convex semi-uniform polychoron that is a variant of the rectified tesseract with demitesseractic symmetry. As such it can be represented by x3o3o *b3y, and has 16 tetrahedra (of two types, sizes x and y) and 8 rhombitetrahedra (type x3o3y) as cells, with two edge lengths.

## Vertex coordinates[edit | edit source]

A small rhombated demitesseract with edge lengths a and b has vertices given by all permutations and even sign changes of:

Alternative coordinates in a different orientation can be given by all even sign changes and permutations of: