# Augmented triangular prism

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Augmented triangular prism | |
---|---|

Rank | 3 |

Type | CRF |

Space | Spherical |

Notation | |

Bowers style acronym | Autip |

Coxeter diagram | oxx oxo&#xt |

Elements | |

Faces | 2+2+2 triangles, 2 squares |

Edges | 1+2+2+4+4 |

Vertices | 1+2+4 |

Vertex figures | 1 square, edge length 1 |

4 trapezoids, edge lengths 1, 1, 1, √2 | |

2 isosceles triangles, edge lengths 1, √2, √2 | |

Measures (edge length 1) | |

Volume | |

Dihedral angles | 3–3 join: |

3–4 join: | |

3–3 pyramidal: | |

3–4 prismatic: 90° | |

4–4: 60° | |

Central density | 1 |

Number of external pieces | 8 |

Level of complexity | 13 |

Related polytopes | |

Army | Autip |

Regiment | Autip |

Dual | Lateromonotruncated triangular tegum |

Conjugate | Excavated triangular prism |

Abstract & topological properties | |

Flag count | 52 |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | K_{2}×I, order 4 |

Convex | Yes |

Nature | Tame |

The **augmented triangular prism** is one of the 92 Johnson solids (J_{49}). It consists of 2+2+2 triangles and 2 squares. It can be constructed by attaching a square pyramid to one of the square faces of the triangular prism.

## Vertex coordinates[edit | edit source]

An augmented triangular prism of edge length 1 has the following vertices:

## In vertex figures[edit | edit source]

The augmented triangular prism appears as the vertex figure of the nonuniform digonal-triangular duoantiprism. This vertex figure has an edge length of 1, and has no corealmic realization, because the Johnson augmented triangular prism has no circumscribed sphere.

Variants made by changing the edge opposite to the vertex also appear as the vertex figure of the nonuniform duoantiprisms made out of a dyad and a regular polygon.

## External links[edit | edit source]

- Klitzing, Richard. "autip".

- Quickfur. "The Augmented Triangular Prism".

- Wikipedia Contributors. "Augmented triangular prism".
- McCooey, David. "Augmented Triangular Prism"