# Compound of two pentagonal prisms

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Compound of two pentagonal prisms | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Coxeter diagram | xo5ox xx |

Elements | |

Components | 2 pentagonal prisms |

Faces | 10 squares, 4 pentagons as 2 stellated decagons |

Edges | 10+20 |

Vertices | 20 |

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

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 4–4: 108° |

4–5: 90° | |

Height | 1 |

Central density | 2 |

Number of external pieces | 22 |

Level of complexity | 6 |

Related polytopes | |

Army | Semi-uniform Dip, edge lengths (base), 1 (sides) |

Regiment | * |

Dual | Compound of two pentagonal tegums |

Conjugate | Compound of two pentagrammic prisms |

Abstract & topological properties | |

Flag count | 120 |

Orientable | Yes |

Properties | |

Symmetry | I_{2}(10)×A_{1}, order 40 |

Convex | No |

Nature | Tame |

The **stellated decagonal prism** or **compound of two pentagonal prisms** is a prismatic uniform polyhedron compound. It consists of 2 stellated decagons and 10 squares. Each vertex joins one stellated decagon and two squares. As the name suggests, it is a prism based on a stellated decagon.

Its quotient prismatic equivalent is the pentagonal antiprismatic prism, which is four-dimensional.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a stellated decagonal prism of edge length 1 centered at the origin are given by:

## Variations[edit | edit source]

This compound has variants where the bases are non-regular compounds of two pentagons. In these cases the compound has only pentagonal prismatic symmetry and the convex hull is a dipentagonal prism.