# Tetratriangle

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Tetratriangle | |
---|---|

Rank | 2 |

Type | Regular |

Space | Spherical |

Notation | |

Bowers style acronym | Tetri |

Schläfli symbol | {12/4} |

Elements | |

Components | 4 triangles |

Edges | 12 |

Vertices | 12 |

Vertex figure | Dyad, length 1 |

Measures (edge length 1) | |

Circumradius | |

Inradius | |

Area | |

Angle | 60° |

Central density | 4 |

Number of external pieces | 24 |

Level of complexity | 2 |

Related polytopes | |

Army | Dog, edge length |

Dual | Tetratriangle |

Conjugate | Tetratriangle |

Convex core | Dodecagon |

Abstract & topological properties | |

Flag count | 24 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | I_{2}(12), order 24 |

Convex | No |

Nature | Tame |

The **tetratriangle**, or **tetri**, is a polygon compound composed of 4 triangles. As such it has 12 edges and 12 vertices.

It is the third stellation of the dodecagon.

Its quotient prismatic equivalent is the triangular tetrahedroorthowedge, which is five-dimensional.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a tetratriangle of edge length 1 centered at the origin are given by:

## Variations[edit | edit source]

The tetratriangle can be varied by seeing it as a compound of 2 hexagrams and changing the angle between the two component hexagrams from the usual 30°. These 4-triangle compounds generally have a dihexagon as their convex hull and remain uniform, but not regular, with hexagonal symmetry only.

## External links[edit | edit source]

- Bowers, Jonathan. "Regular Polygons and Other Two Dimensional Shapes".