# Elongated pentagonal pyramid

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Elongated pentagonal pyramid | |
---|---|

Rank | 3 |

Type | CRF |

Space | Spherical |

Notation | |

Bowers style acronym | Epeppy |

Coxeter diagram | oxx5ooo&#xt |

Elements | |

Faces | 5 triangles, 5 squares, 1 pentagon |

Edges | 5+5+5+5 |

Vertices | 1+5+5 |

Vertex figures | 1 pentagon, edge length 1 |

5 kites, edge lengths 1 and √2 | |

5 isosceles triangles, edge lengths (1+√5)/2, √2, √2 | |

Measures (edge length 1) | |

Volume | |

Dihedral angles | 3–3: |

3–4: | |

4–4: 108° | |

4–5: 90° | |

Central density | 1 |

Related polytopes | |

Army | Epeppy |

Regiment | Epeppy |

Dual | Elongated pentagonal pyramid |

Conjugate | Elongated pentagrammic pyramid |

Abstract properties | |

Euler characteristic | 2 |

Topological properties | |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | H_{2}×I, order 10 |

Convex | Yes |

Nature | Tame |

The **elongated pentagonal pyramid** is one of the 92 Johnson solids (J_{9}). It consists of 5 triangles, 5 squares, and 1 pentagon. It can be constructed by attaching a pentagonal prism to the base of the pentagonal pyramid..

If a second pyramid is attached to the other base of the pentagonal prism, the result is the elongated pentagonal bipyramid.

## Vertex coordinates[edit | edit source]

An elongated pentagonal pyramid of edge length 1 has the following vertices:

## External links[edit | edit source]

- Klitzing, Richard. "epeppy".

- Quickfur. "The Elongated Pentagonal Pyramid".

- Wikipedia Contributors. "Elongated pentagonal pyramid".
- McCooey, David. "Elongated Pentagonal Pyramid"