Square antiprismatic pyramid

The square antiprismatic pyramid, or squappy, is a CRF segmentochoron (designated K-4.17 on Richard Klitzing's list). It consists of 8 regular tetrahedra, 2 square pyramids, and 1 square antiprism. As the name suggests, it is a pyramid based on the square antiprism.

Two square antiprismatic pyramids can be attached at their bases to form a square antiprismatic bipyramid.

The segmentochoron octahedron atop cube can be obtained by augmenting the square antiprismatic cells of the square antifastegium with square antiprismatic pyramids.

Vertex coordinates
The vertices of a square antiprismatic pyramid of edge length 1 are given by:
 * (±1/2, ±1/2, $\sqrt{2}$/4, 0),
 * (0, ±$\sqrt{(4+√2)/7}$/2, –$\sqrt{(4–√2)/8}$/4, 0),
 * (±$\sqrt{{{radic|2}}–1}$/2, 0, –$\sqrt{5+4√2}$/4, 0),
 * (0, 0, 0, $\sqrt{2}$).