28th Johnson solid; 2 square cupolae joined base-to-base
Square orthobicupola
Type
Johnson J27 – J28 – J29
Faces
8 triangles 2+8 squares
Edges
32
Vertices
16
Vertex configuration
8(32.42) 8(3.43)
Symmetry group
D4h
Dual polyhedron
-
Properties
convex
Net
In geometry, the square orthobicupola is one of the Johnson solids (J28). As the name suggests, it can be constructed by joining two square cupolae (J4) along their octagonal bases, matching like faces. A 45-degree rotation of one cupola before the joining yields a square gyrobicupola (J29).
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 (J15), which itself is merely an elongated octahedron.
It can be constructed from the disphenocingulum (J90) by replacing the band of up-and-down triangles by a band of rectangles, while fixing two opposite sphenos.
^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.
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