# Compound of twelve pentagrammic retroprisms

Compound of twelve pentagrammic retroprisms | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Gidasid |

Elements | |

Components | 12 pentagrammic retroprisms |

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

Edges | 120+120 |

Vertices | 120 |

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

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 3–3: |

5/2–3: | |

Central density | 36 |

Related polytopes | |

Army | Semi-uniform Grid |

Regiment | Gidasid |

Dual | Compound of twelve pentagrammic concave antitegums |

Conjugate | Compound of twelve pentagonal antiprisms |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | H_{3}, order 120 |

Convex | No |

Nature | Tame |

The **great inverted disnub dodecahedron**, **gidasid**, or **compound of twelve pentagrammic retroprisms** is a uniform polyhedron compound. It consists of 120 triangles and 24 pentagrams (whcih fall in pairs in the same plane and combine into 12 stellated decagrams), with one pentagram and three triangles joining at a vertex.

This compound has rotational freedom, represented by an angle θ. we start at θ = 0° with all the pentagrammic retroprisms inscribed in a great icosahedron, and rotate pairs of retroprisms in opposite directions. At θ = 36° the retroprisms coincide by pairs, resulting in a double cover of the great inverted snub dodecahedron.

## Vertex coordinates[edit | edit source]

The vertices of a great inverted disnub dodecahedron of edge length 1 and rotation angle θ are given by all even permutations of:

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category C8: Antiprismatics" (#51).

- Klitzing, Richard. "gidasid".
- Wikipedia contributors. "Compound of twelve pentagrammic crossed antiprisms with rotational freedom".