# Compound of twelve pentagrammic antiprisms

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Compound of twelve pentagrammic antiprisms | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Sadsid |

Elements | |

Components | 12 pentagrammic antiprisms |

Faces | 120 triangles, 24 pentagrams as 12 stellated decagrams |

Edges | 120+120 |

Vertices | 60 |

Vertex figure | Isosceles trapezoid, edge length 1, 1, 1, (√5–1)/2 |

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 5/2–3: |

3–3: | |

Central density | 24 |

Number of external pieces | 1380 |

Level of complexity | 82 |

Related polytopes | |

Army | Semi-uniform Grid |

Regiment | Sadsid |

Dual | Compound of twelve pentagrammic antitegums |

Conjugate | Compound of twelve pentagrammic antiprisms |

Convex core | Disdyakis triacontahedron |

Abstract & topological properties | |

Flag count | 960 |

Orientable | Yes |

Properties | |

Symmetry | H_{3}, order 120 |

Convex | No |

Nature | Tame |

The **small disnub dodecahedron**, **sadsid**, or **compound of twelve pentagrammic antiprisms** is a uniform polyhedron compound. It consists of 120 triangles and 24 pentagrams (which fall in pairs into the same planes combining into 12 stellated decagrams), with one pentagram and three triangles joining at a vertex.

It can be formed by combining the two chiral forms of the small snub dodecahedron.

Its quotient prismatic equivalent is the pentagrammic antiprismatic dodecadakoorthowedge, which is fourteen-dimensional.

## Vertex coordinates[edit | edit source]

The vertices of a small disnub dodecahedron of edge length 1 are given by all even permutations of:

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category C8: Antiprismatics" (#53).

- Klitzing, Richard. "sadsid".
- Wikipedia contributors. "Compound of twelve pentagrammic antiprisms".