# Great chirorhombidodecahedron

The **great chirorhombidodecahedron**, **gikrid**, or **compound of six pentagrammic prisms** is a uniform polyhedron compound. It consists of 30 squares and 12 pentagrams, with one pentagram and two squares joining at a vertex.

Great chirorhombidodecahedron | |
---|---|

Rank | 3 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Gikrid |

Elements | |

Components | 6 pentagrammic prisms |

Faces | 30 squares, 12 pentagrams |

Edges | 30+60 |

Vertices | 60 |

Vertex figure | Isosceles triangle, edge lengths (√5–1)/2, √2, √2 |

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 4–5/2: 90° |

4–4: 36° | |

Central density | 12 |

Number of external pieces | 192 |

Level of complexity | 38 |

Related polytopes | |

Army | Srid |

Regiment | Gikrid |

Dual | Compound of six pentagrammic tegums |

Conjugate | Chirorhombidodecahedron |

Convex core | Rhombic triacontahedron |

Abstract & topological properties | |

Flag count | 360 |

Orientable | Yes |

Properties | |

Symmetry | H_{3}+, order 60 |

Convex | No |

Nature | Tame |

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

## Vertex coordinatesEdit

The vertices of a great chirorhombidodecahedron of edge length 1 are given by all permutations of:

plus all even permutations of:

This compound is chiral. The compound of the two enantiomorphs is the great disrhombidodecahedron.

## External linksEdit

- Bowers, Jonathan. "Polyhedron Category C7: Chiral and Doubled Prismatics" (#42).

- Klitzing, Richard. "gikrid".

- Wikipedia Contributors. "Compound of six pentagrammic prisms".