J27 - J28 - J29
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 regular-faced polyhedra, but which is not uniform, i.e., not a Platonic solid, Archimedean solid, prism or antiprism. They are named by Norman Johnson who first enumerated the set in 1966.
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.
- Weisstein, Eric W., "Johnson solid", MathWorld.
- Weisstein, Eric W., "Square orthobicupola", MathWorld.
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