# Sesquitruncated octahedron

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Sesquitruncated octahedron | |
---|---|

Rank | 3 |

Type | Near-miss |

Space | Spherical |

Elements | |

Faces | 24 isosceles triangles, 6 squares, 8 triangular-symmetric enneagons |

Edges | 12+24+48 |

Vertices | 24+24 |

Vertex figures | 24 isosceles triangles |

24 isosceles trapezoids | |

Measures (based on regular enneagons of edge length 1) | |

Edge length ratio | |

Circumradius | |

Central density | 1 |

Number of external pieces | 38 |

Related polytopes | |

Conjugate | None |

Abstract & topological properties | |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | B_{3}, order 48 |

Convex | Yes |

Nature | Tame |

The **sesquitruncated octahedron** is a near-miss Johnson solid. Its faces are 24 isosceles triangles, 6 squares and 8 enneagons.

To construct it, one needs to inscribe an enneagon in every face of a regular octahedron and fill all the remaining gaps with triangles and squares.

The sesquitruncated octahedron is a cell of the sesquitruncated rectified cubic honeycomb which is a **near-miss** CRF honeycomb.

Its other cell types are: sesquitruncated cuboctahedra, deformed cuboctahedra and deformed tetrahedra.

## Variations[edit | edit source]

There is one variant of the sesquitruncated octahedron with regular enneagons. If the edge length of the enneagon is 1, the other edge length is ≈ 1.04967.