# Small trisoctachoron

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Small trisoctachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Sto |

Elements | |

Cells | 8 tetrahedra, 8 truncated tetrahedra, 8 octahemioctahedra |

Faces | 32+32 triangles, 32 hexagons |

Edges | 48+48 |

Vertices | 32 |

Vertex figure | Crossed triangular cuploid, edge lengths 1 (top triangle and base pseudo-triangle) and √3 (sides) |

Measures (edge length 1) | |

Circumradius | |

Dichoral angles | Oho–3–tet: 120° |

Oho–6–tut: 120° | |

Oho–3–tut: 60° | |

Number of external pieces | 248 |

Level of complexity | 36 |

Related polytopes | |

Army | Rit |

Regiment | Rit |

Conjugate | None |

Abstract & topological properties | |

Flag count | 1536 |

Euler characteristic | 8 |

Orientable | No |

Properties | |

Symmetry | D_{4}, order 192 |

Flag orbits | 8 |

Convex | No |

Nature | Tame |

The **small trisoctachoron**, or **sto**, is a nonconvex uniform polychoron that consists of 8 tetrahedra, 8 octahemioctahedra, and 8 truncated tetrahedra. One tetrahedron, three octahemioctahedra, and three truncated tetrahedra join at each vertex.

It also has 8 tetrahedra as pseudofacets.

It is one of two members of the regiment of the rectified tesseract to have only half the symmetry, the other is the great trisoctachoron.

## 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 12: Podiumverts" (#482).

- Klitzing, Richard. "sto".