# Hexagonal pyramid

Hexagonal pyramid | |
---|---|

Rank | 3 |

Type | CRF |

Space | Euclidean |

Notation | |

Bowers style acronym | Hippy |

Coxeter diagram | ox6oo&#x |

Elements | |

Faces | 6 triangles, 1 hexagon |

Edges | 6+6 |

Vertices | 1+6 |

Vertex figures | 1 hexagon, edge length 1 |

6 isosceles triangles, edge lengths 1, 1, √3 | |

Measures (edge length 1) | |

Circumradius | ∞ |

Volume | 0 |

Dihedral angles | 3-3: 180º |

3-6: 0º | |

Height | 0 |

Number of external pieces | 7 |

Level of complexity | 3 |

Related polytopes | |

Army | Hippy |

Regiment | Hippy |

Dual | Hexagonal pyramid |

Conjugate | None |

Abstract & topological properties | |

Flag count | 48 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | G_{2}×I, order 12 |

Convex | Yes |

Net count | 32 |

Nature | Tame |

The **hexagonal pyramid**, or **hippy**, is a pyramid with a hexagonal base and 6 triangles as sides. The version with equilateral triangles as sides is flat, as a regular hexagon can be exactly decomposed into 6 equilateral triangles by a central point. Other variants with isosceles triangles as sides exist as non-degenerate polyhedra.

The flat variant with equilateral triangles is the vertex-first cap of the triangular tiling.

## Vertex coordinates[edit | edit source]

A hexagonal pyramid of edge length 1 has the following vertices:

These coordinates are a subset of the vertices of the regular triangular tiling.

## Representations[edit | edit source]

A hexagonal pyramid has the following Coxeter diagrams:

- ox6oo&#x (full symmetry)
- ox3ox&#x (generally a ditrigonal pyramid)

## General variant[edit | edit source]

For the general hexagonal pyramid with base edges of length b and lacing edges of length l, its height is given by , its circumradius by , and its volume is given by .

## External links[edit | edit source]

- Klitzing, Richard. "hippy".
- Wikipedia contributors. "Hexagonal pyramid".