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).
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.
It can be constructed from the disphenocingulum (J_90) by replacing the band of up-and-down triangles by a band of rectangles, while fixing two opposite sphenos.
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.
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In geometry, a bicupola is a solid formed by connecting two cupolae on their bases. There are two classes of bicupola because each cupola (bicupola half) is bordered by alternating triangles and squares. If similar faces are attached together the result is an orthobicupola; if squares are attached to triangles it is a gyrobicupola. Cupolae and bicupolae categorically exist as infinite sets of polyhedra, just like the pyramids, bipyramids, prisms, and trapezohedra.
In geometry, a Johnson solid is a strictly convex polyhedron each face of which is a regular polygon. There is no requirement that each face must be the same polygon, or that the same polygons join around each vertex. An example of a Johnson solid is the square-based pyramid with equilateral sides (J_1); it has 1 square face and 4 triangular faces. Some authors require that the solid not be uniform (i.e., not Platonic solid, Archimedean solid, uniform prism, or uniform antiprism) before they refer to it as a "Johnson solid".