# Complex dipentagon

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Complex dipentagon | |
---|---|

Rank | 2 |

Type | Semi-uniform |

Elements | |

Edges | 5 + 5 |

Vertices | 5 |

Vertex figure | Tetrad |

Measures (minor edge length 1) | |

Edge lengths | Pentagonal edges (5): 1 |

Pentagrammic edges (5): | |

Circumradius | |

Perimeter | |

Central density | 3 |

Related polytopes | |

Army | Peg |

Dual | Mermin's pentagram |

Conjugate | Complex dipentagon |

Convex core | Pentagon |

Abstract & topological properties | |

Flag count | 20 |

Configuration symbol | (5_{4}, 10_{2}) |

Skeleton | K_{5} |

Properties | |

Symmetry | H_{2}, order 10 |

Convex | No |

Nature | Exotic |

The **complex dipentagon** is a semi-uniform exotic polygonoid. It has 10 edges of two different lengths, with 2 of each at a vertex making a tetrad vertex figure. It is semi-uniform, however if conjugacies are included in its symmetry it becomes regular.

It can be seen as a compound of a pentagon and a pentagram, with their vertices coinciding and merging into tetradic vertices.

## Related polytopoids[edit | edit source]

### As a vertex figure[edit | edit source]

The complex dipentagon appears as the vertex figure of both the small complex icosidodecahedron and the great complex icosidodecahedron