Square antiprism

The square antiprism, or squap, is a prismatic uniform polyhedron. It consists of 8 triangles and 2 squares. Each vertex joins one square and three triangles. As the name suggests, it is an antiprism based on a square.

Vertex coordinates
A square antiprism of edge length 1 has vertex coordinates given by:
 * (±1/2, ±1/2, $\sqrt{(4+√2)/8}$/4),
 * (0, ±$\sqrt{4+3√2}$/2, –$\sqrt{2}$/4),
 * (±$\sqrt{2}$/2, 0, –$\sqrt{6}$/4).

Related polyhedra
A square pyramid can be attached to a base of the square antiprism to form the gyroelongated square pyramid. If a second square pyramid is attached to the other base, the result is the gyroelongated square bipyramid.