# Compound of four triangular prisms

(Redirected from Rhomboctahedron)

Compound of four triangular prisms | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Ro |

Elements | |

Components | 4 triangular prisms |

Faces | 8 triangles, 12 squares |

Edges | 12+24 |

Vertices | 24 |

Vertex figure | Isosceles triangle, edge length 1, √2, √2 |

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 4–4: 60° |

4–3: 90° | |

Central density | 4 |

Number of external pieces | 56 |

Level of complexity | 26 |

Related polytopes | |

Army | Non-uniform Snic, edge lengths (squares), (equilateral triangles), (between scalene triangles) |

Regiment | Ro |

Dual | Compound of four triangular tegums |

Conjugate | Compound of four triangular prisms |

Convex core | Rhombic dodecahedron |

Abstract & topological properties | |

Flag count | 144 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}+, order 24 |

Convex | No |

Nature | Tame |

The **rhomboctahedron**, **ro**, or **compound of four triangular prisms** is a uniform polyhedron compound. It consists of 12 squares and 8 triangles, with one triangle and two squares joining at a vertex.

Its quotient prismatic equivalent is the triangular prismatic tetrahedroorthowedge, which is six-dimensional.

## Vertex coordinates[edit | edit source]

The vertices of a rhomboctahedron of edge length 1 are given by all even sign changes and even permutations, plus all odd sign changes and odd permutatoins, of:

- .

## Related polyhedra[edit | edit source]

This compound is chiral. The compound of the two enantiomorphs is the disrhomboctahedron.

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category C7: Chiral and Doubled Prismatics" (#38).

- Klitzing, Richard. "ro".
- Wikipedia contributors. "Compound of four triangular prisms".