Square antiprism

When eight points are distributed on the surface of a sphere with the aim of maximising the distance between them in some sense, the resulting shape corresponds to a square antiprism rather than a cube.

According to the VSEPR theory of molecular geometry in chemistry, which is based on the general principle of maximizing the distances between points, a square antiprism is the favoured geometry when eight pairs of electrons surround a central atom.

[3] In addition, the element sulfur forms octatomic S8 molecules as its most stable allotrope.

It is not a true antiprism because of its taper: the top square has half the area of the bottom one.

The square antiprism is first in a series of snub polyhedra and tilings with vertex figure 3.3.4.3.n.