# Small rhombidodecacron

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Small rhombidodecacron | |
---|---|

Rank | 3 |

Type | Uniform dual |

Notation | |

Coxeter diagram | m5/2m5m () |

Elements | |

Faces | 60 butterflies |

Edges | 60+60 |

Vertices | 12+30 |

Vertex figure | 30 squares, 12 decagons |

Measures (edge length 1) | |

Inradius | |

Dihedral angle | |

Central density | odd |

Number of external pieces | 120 |

Related polytopes | |

Dual | Small rhombidodecahedron |

Conjugate | Great rhombidodecacron |

Convex core | Deltoidal hexecontahedron |

Abstract & topological properties | |

Flag count | 480 |

Euler characteristic | –18 |

Orientable | No |

Genus | 20 |

Properties | |

Symmetry | H_{3}, order 120 |

Convex | No |

Nature | Tame |

The **small rhombidodecacron** is a uniform dual polyhedron. It consists of 60 butterflies.

It appears the same as the small dodecacronic hexecontahedron.

If its dual, the small rhombidodecahedron, has an edge length of 1, then the short edges of the butterflies will measure , and the long edges will be . The butterflies have two interior angles of , and two of . The intersection has an angle of .

## Vertex coordinates[edit | edit source]

A small rhombidodecacron with dual edge length 1 has vertex coordinates given by all even permutations of:

- ,
- ,
- .

## External links[edit | edit source]

- Wikipedia contributors. "Small rhombidodecacron".
- McCooey, David. "Small Rhombidodecacron"