# Small rhombicuboctahedron atop truncated cube

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Small rhombicuboctahedron atop truncated cube | |
---|---|

Rank | 4 |

Type | Segmentotope |

Notation | |

Bowers style acronym | Sircoatic |

Coxeter diagram | xx4xo3ox&#x |

Elements | |

Cells | 12 triangular prisms, 8 octahedra, 6 square cupolas, 1 small rhombicuboctahedron, 1 truncated cube |

Faces | 8+8+24+24 triangles, 6+12+24 squares, 6 octagons |

Edges | 12+24+24+24+48 |

Vertices | 24+24 |

Vertex figures | 24 square wedges, edge lengths 1 (base square) and √2 (top edge and sides) |

24 skewed square pyramids, base edge lengths 1, side edge lengths √2+√2 and √2 | |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Oct–3–trip: 150° |

Sirco–4–trip: | |

Squacu–4–trip: | |

Sirco–3–oct: 120° | |

Squacu–3–oct: 120° | |

Sirco–4–squacu: 90° | |

Tic–8–squacu: 90° | |

Tic–3–oct: 60° | |

Height | |

Central density | 1 |

Related polytopes | |

Army | Sircoatic |

Regiment | Sircoatic |

Dual | Deltoidal icositetrahedral-triakis octahedral tegmoid |

Conjugate | Quasirhombicuboctahedron atop quasitruncated hexahedron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}×I, order 48 |

Convex | Yes |

Nature | Tame |

**Small rhombicuboctahedron atop truncated cube**, or **sircoatic**, is a CRF segmentochoron (designated K-4.100 on Richard Klitzing's list). As the name suggests, it consists of a small rhombicuboctahedron and a truncated cube as bases, connected by 12 triangular prisms, 8 octahedra, and 6 square cupolas.

Two small rhombicuboctahedron atop truncated cube segmentochora can be attached to the bases of a truncated cubic prism to form a small rhombated tesseract, as the square cupolas of the caps fuse with the octagonal prisms of the truncated cubic prism to form further small rhombicuboctahedra.

## Vertex coordinates[edit | edit source]

The vertices of a small rhombicuboctahedron atop truncated cube segmentochoron of edge length 1 are given by:

- and all permutations of first three coordinates
- and all permutations of first three coordinates

## External links[edit | edit source]

- Klitzing, Richard. "sircoatic".