# Compound of six pentagrammic retroprisms

Compound of six pentagrammic retroprisms | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Gissed |

Elements | |

Components | 6 pentagrammic retroprisms |

Faces | 60 triangles, 12 pentagrams |

Edges | 60+60 |

Vertices | 60 |

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 | 18 |

Number of external pieces | 1272 |

Level of complexity | 83 |

Related polytopes | |

Army | Semi-uniform Tid, edge lengths (triangles), (between dipentagons) |

Regiment | Gissed |

Dual | Compound of six pentagrammic concave antitegums |

Conjugate | Compound of six pentagonal antiprisms |

Convex core | Pentakis dodecahedron |

Abstract & topological properties | |

Flag count | 480 |

Orientable | Yes |

Properties | |

Symmetry | H_{3}, order 120 |

Convex | No |

Nature | Tame |

The **great inverted snub dodecahedron**, **gissed**, or **compound of six pentagrammic retroprisms** is a uniform polyhedron compound. It consists of 60 triangles and 12 pentagrams, with one pentagram and three triangles joining at a vertex.

This compound can be formed by inscribing six pentagrammic retroprisms within a great icosahedron (each by removing one pair of opposite vertices) and then rotating each retroprism by 36° around its axis.

Its quotient prismatic equivalent is the pentagrammic retroprismatic hexateroorthowedge, which is eight-dimensional.

A double cover of this compound occurs as a special case of the great inverted disnub dodecahedron.

## Vertex coordinates[edit | edit source]

The vertices of a great inverted snub dodecahedron of edge length 1 are given by all even permutations of:

- ,
- ,
- .

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category C8: Antiprismatics" (#50).

- Klitzing, Richard. "gissed".
- Wikipedia contributors. "Compound of six pentagrammic crossed antiprisms".