# Blend of 2 triangular prisms

Blend of 2 triangular prisms | |
---|---|

Rank | 3 |

Type | Segmentotope |

Notation | |

Bowers style acronym | Tutrip |

Elements | |

Faces | 4 triangles, 4 squares |

Edges | 2+4+8 |

Vertices | 4+4 |

Vertex figures | 4 isosceles triangles, edge lengths 1, √2, √2 |

4 butterflies, edge lengths 1 and √2 | |

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 3-4 (trip edges): 90° |

4–4: 60° | |

3-4 (at pseudo {4}): 30° | |

Height | Stellated square atop pseudo square: |

Related polytopes | |

Army | Square antipodium |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | B_{2}×I, order 8 |

Convex | No |

Nature | Tame |

The **blend of 2 triangular prisms**, or **tutrip**, is a segmentohedron. It consists of 4 triangles and 4 squares. It is a cupolaic blend of two triangular prisms seen as digonal cupolae sharing a square face which blends out.

It is a segmentohedron as a stellated square (a degenerate compound of 2 perpendicular edges) atop pseudo square. It is notable for showing up as a cell in many scaliform polytopes, and is one of the simplest orbiform polyhedra that can be constructed only as a blend, rather than by removing vertices from a larger polyhedron.

It is isomorphic to the gyrobifastigium.

It has multiple analogues in higher dimensions, such as the blend of 3 square pyramidal prisms and blend of 3 triangular-square duoprisms in 4D.

It is the 4-4-3 acrohedron generated by Green's rules.

## Vertex coordinates[edit | edit source]

A tutrip of edge length 1 has vertex coordinates given by:

- ,
- ,
- .

## External links[edit | edit source]

- Klitzing, Richard. "tutrip".