# Triangular gyroprism

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Triangular gyroprism | |
---|---|

Rank | 3 |

Type | Isogonal |

Space | Spherical |

Notation | |

Bowers style acronym | Trigyp |

Coxeter diagram | s2s3s |

Elements | |

Faces | 6 scalene triangles, 2 equilateral triangles |

Edges | 3+3+6 |

Vertices | 6 |

Vertex figure | Irregular tetragon |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Army | Trigyp |

Regiment | Trigyp |

Dual | Triangular gyrotegum |

Conjugate | Triangular gyroprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | (A_{2}×A_{1})+, order 6 |

Convex | Yes |

Nature | Tame |

The **triangular gyroprism**, or **trigyp**, is a triangle-based gyroprism, a variant of the triangular antiprism where the bases are rotated by an angle other than 60°, and has 6 scalene triangles for its sides instead of isosceles triangles. It can be formed by alternating a ditrigonal prism.

A concave variant of the triangular gyroprism is the Schönhardt polyhedron, the simplest non-convex polyhedron that cannot be triangulated into tetrahedra.