# Bowtie tegum

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Bowtie tegum | |
---|---|

Rank | 3 |

Type | Orbiform |

Space | Spherical |

Notation | |

Bowers style acronym | Bobipyr |

Elements | |

Faces | 4 triangles, 2 squares |

Edges | 2+8 |

Vertices | 2+4 |

Vertex figures | 2 bowties, edge lengths 1, √2 |

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

Measures (edge length 1) | |

Circumradius | |

Dihedral angles | 3-3: |

3-4: | |

Related polytopes | |

Army | Oct |

Dual | Bowtie tegum (abstract) |

Conjugate | None |

Abstract & topological properties | |

Flag count | 40 |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | K_{3}, order 8 |

Convex | No |

Nature | Tame |

The **bowtie tegum**, also called the **bowtie bipyramid** or **bobipyr**, is an orbiform polyhedron. It is an edge-faceting of the octahedron, using 4 of its triangles and 2 of the central squares of the tetrahemihexahedron. The abstract bowtie tegum would have two pairs of triangles which in this polyhedron merge into squares.

This polyhedron is abstractly self-dual.

It appears as a cell in some scaliform polychora of the hexadecachoron regiment: the skew octahemioctachoron, the hemitesseractihemioctachoron, and the sesquitesseractihemioctachoron.

## Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the octahedron.

## External links[edit | edit source]

- Bowers, Jonathan. "Batch 1: Oct and Co Facetings" (#4 under oct).

- Klitzing, Richard. "bobipyr".