# Triakis triangular tegum

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Triakis triangular tegum | |
---|---|

Rank | 3 |

Elements | |

Faces | 6 isosceles triangles, 12 scalene triangles |

Edges | 3+6+6+12 |

Vertices | 2+3+6 |

Vertex figures | 2 triambi |

3 rectangular-symmetric octagons | |

6 isosceles triangles | |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | Truncated triangular prism |

Abstract & topological properties | |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | A_{2}×A_{1}, order 12 |

Convex | Yes |

Nature | Tame |

The **triakis triangular tegum** is a polyhedron formed from the triangular tegum by augmenting its faces with shallow triangular pyramids. It has 6 isosceles triangles and 12 scalene triangles as faces.

The canonical variant with midradius 1 has four edge lengths: one of length , one of length , one of length and the other of length .

## Vertex coordinates[edit | edit source]

The vertices of a canonical triakis triangular tegum of midradius 1 are given by:

## In vertex figures[edit | edit source]

A variant of the triakis triangular tegum with (A_{2}×A_{1})+ symmetry occurs as the vertex figure of the tetrafold tetraswirlchoron.