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, ±$\sqrt{2√2}$/2, –$\sqrt{4+3√2}$/4),
 * (±$\sqrt{2}$/2, 0, –$\sqrt{2}$/4).

Representations
A square antiprism has the following Coxeter diagrams:


 * s2s8o (alternated octagonal prism)
 * s2s4s (alternated ditetragonal prism)
 * xo4ox&#x (bases considered separately)

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.

Two non-prismatic uniform polyhedron compounds are composed of square antiprisms:


 * Great snub cube (3)
 * Great disnub cube (6)

There are also an infinite amount of prismatic uniform compounds that are the antiprisms of compounds of squares.