Square orthobicupola

The square orthobicupola is one of the 92 Johnson solids (J28). It consists of 8 triangles and 2+8 squares. It can be constructed by attaching two square cupolas at their octagonal bases, such that the two square bases are in the same orientation.

If the cupolas are joined such that the bases are rotated 45°, the result is the square gyrobicupola.

Vertex coordinates
A square orthobicupola of edge length 1 has vertices given by the following coordinates:


 * $$\left(±\frac12,\,±\frac12,\,±\frac{\sqrt2}{2}\right),$$
 * $$\left(±\frac{1+\sqrt2}{2},\,±\frac12,\,0\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}{2},\,0\right).$$

Related polyhedra
An octagonal prism can be inserted between the two halves of the square orthobicupola to produce the elongated square orthobicupola, better known as the uniform small rhombicuboctahedron.