# Compound of twenty tetrahemihexahedra

Compound of twenty tetrahemihexahedra | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Sapisseri |

Elements | |

Components | 20 tetrahemihexahedra |

Faces | 20+60 triangles, 60 squares |

Edges | 60+60+120 |

Vertices | 60 |

Vertex figure | Compound of two bowties, edge lengths 1 and √2 |

Measures (edge length 1) | |

Circumradius | |

Dihedral angle | |

Central density | even |

Related polytopes | |

Army | Semi-uniform srid, edge lengths (pentagons), (triangles) |

Regiment | Gidrid |

Dual | Compound of twenty tetrahemihexacrons |

Conjugate | Compound of twenty tetrahemihexahedra |

Abstract & topological properties | |

Orientable | No |

Properties | |

Symmetry | H_{3}+, order 60 |

Convex | No |

Nature | Tame |

The **snub pseudosnub rhombicosahedron**, **sapisseri**, or **compound of twenty tetrahemihexahedra** is a biformic polyhedron compound. It consists of 20+60 triangles and 60 squares. The vertices coincide in pairs, and thus four triangles and four squares join at each vertex. If the vertices are considered as single compound vertices, this compound is uniform. If they are considered as two separate vertices, it has two vertex orbits.

This compound can be formed by replacing each octahedron in the disnub icosahedron with the tetrahemihexahedron with which it shares its edges. Therefore, it also has the same edges as the great dirhombicosidodecahedron, although it is chiral, unlike either the great dirhombicosidodecahedron or disnub icosahedron.

It can be constructed as a blend of the great dirhombicosidodecahedron and the great snub dodecicosidodecahedron.

## Vertex coordinates[edit | edit source]

Its vertices are the same as those of the disnub icosahedron.

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category C9: Octahedral Continuums" (#67).

- Klitzing, Richard. "sapisseri".
- Wikipedia contributors. "Compound of twenty tetrahemihexahedra".