# Blend of small rhombicosidodecahedron and small rhombidodecahedron

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Blend of small rhombicosidodecahedron and small rhombidodecahedron | |
---|---|

Rank | 3 |

Type | Orbiform |

Space | Spherical |

Elements | |

Faces | 20 triangles, 48 squares, 12 pentagons, 12 decagons |

Edges | 24+48+48+96 |

Vertices | 24+24+48 |

Vertex figures | 12+24 isosceles trapezoids, edge lengths 1, √2, (1+√5)/2, √2 |

12+24 butterflies, edge lengths √2 and √(5+√5)/2 | |

24 (3.4.5.10.4.10) | |

Measures (edge length 1) | |

Circumradius | |

Related polytopes | |

Conjugate | Blend of quasirhombicosidodecahedron and great rhombidodecahedron |

Convex core | Dodecahedron, edge length (5-√5)/2 |

Abstract & topological properties | |

Flag count | 864 |

Euler characteristic | –28 |

Orientable | No |

Genus | 30 |

Properties | |

Symmetry | B_{3}/2, order 24 |

Convex | No |

Nature | Tame |

The **blend of small rhombicosidodecahedron and small rhombidodecahedron** is an orbiform polyhedron. It consists of 20 triangles, 48 squares, 12 pentagons, and 12 decagons. As the name suggests, it can be constructed by blending a small rhombicosidodecahedron and a small rhombidodecahedron together by six square faces.

## Vertex coordinates[edit | edit source]

A blend of small rhombicosidodecahedron and small rhombidodecahedron of edge length 1 has vertex coordinates given by all permutations of

## Related polytopes[edit | edit source]

The blend of small rhombicosidodecahedron and small rhombidodecahedron appears as a cell in several scaliform polychora. These include the: