# Square orthobicupola

Square orthobicupola | |
---|---|

Type | JohnsonJ_{27} - J - J_{28}_{29} |

Faces | 8 triangles 2+8 squares |

Edges | 32 |

Vertices | 16 |

Vertex configuration | 8(3^{2}.4^{2})8(3.4 ^{3}) |

Symmetry group | D_{4h} |

Dual polyhedron | - |

Properties | convex |

Net | |

In geometry, the **square orthobicupola** is one of the Johnson solids (*J*_{28}). As the name suggests, it can be constructed by joining two square cupolae (*J*_{4}) along their octagonal bases, matching like faces. A 45-degree rotation of one cupola before the joining yields a square gyrobicupola (*J*_{29}).

A Johnson solid is one of 92 strictly convex polyhedra that is composed of regular polygon faces but are not uniform polyhedra (that is, they are not Platonic solids, Archimedean solids, prisms, or antiprisms). They were named by Norman Johnson, who first listed these polyhedra in 1966.^{[1]}

The *square orthobicupola* is the second in an infinite set of orthobicupolae.

The square orthobicupola can be elongated by the insertion of an octagonal prism between its two cupolae to yield a rhombicuboctahedron, or collapsed by the removal of an irregular hexagonal prism to yield an elongated square dipyramid (*J*_{15}), which itself is merely an elongated octahedron.

## Related polyhedra and honeycombs[edit]

The square orthobicupola forms space-filling honeycombs with tetrahedra; with cubes and cuboctahedra; with tetrahedra and cubes; with square pyramids, tetrahedra and various combinations of cubes, elongated square pyramids and/or elongated square bipyramids.^{[2]}

## References[edit]

**^**Johnson, Norman W. (1966), "Convex polyhedra with regular faces",*Canadian Journal of Mathematics*,**18**: 169–200, doi:10.4153/cjm-1966-021-8, MR 0185507, Zbl 0132.14603.**^**http://woodenpolyhedra.web.fc2.com/J28.html

## External links[edit]

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