# Biaugmented triangular prism

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Biaugmented triangular prism | |
---|---|

Rank | 3 |

Type | CRF |

Notation | |

Bowers style acronym | Bautip |

Elements | |

Faces | 2+2+2+4 triangles, 1 square |

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

Vertices | 2+2+4 |

Vertex figures | 2 squares, edge length 1 |

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

2 pentagons, edge length 1 | |

Measures (edge length 1) | |

Volume | |

Dihedral angles | 3–3 double join: |

3–3 single join: | |

3–4 join: | |

3–3 pyramidal: | |

3–4 prismatic: 90° | |

Central density | 1 |

Number of external pieces | 11 |

Level of complexity | 17 |

Related polytopes | |

Army | Bautip |

Regiment | Bautip |

Dual | Laterobitruncated triangular tegum |

Conjugate | Biaugmented triangular prism |

Abstract & topological properties | |

Flag count | 68 |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | K_{2}×I, order 4 |

Convex | Yes |

Nature | Tame |

The **biaugmented triangular prism** is one of the 92 Johnson solids (J_{50}). It consists of 2+2+2+4 triangles and 1 square. It can be constructed by attaching square pyramids to two of the square faces of the triangular prism.

## Vertex coordinates[edit | edit source]

A biaugmented triangular prism of edge length 1 has the following vertices:

## In vertex figures[edit | edit source]

Variants of the biaugmented triangular prism (in its symmetry axis, with non-base connected edge lengths of √2) by changing the edge opposite to the square appear as the vertex figure of the nonuniform antiditetragoltriate, and has no corealmic realization.

## External links[edit | edit source]

- Klitzing, Richard. "bautip".
- Quickfur. "The Biaugmented Triangular Prism".

- Wikipedia contributors. "Biaugmented triangular prism".
- McCooey, David. "Biaugmented Triangular Prism"