Triangular antiprism

The triangular antiprism is a triangle-based antiprism. The version with all equal edges is the regular octahedron, one of the Platonic solids, but other versions exist with isosceles triangles as their sides. In the latter case, their Coxeter diagram could be given as xo3ox&#y.

Vertex coordinates
Cartesian coordinates for a triangular antiprism created from two triangles of edge length b laced by edges of length ℓ, centered at the origin, are given by:
 * ±(0, ($\sqrt{b^{2}+ℓ^{2}}$/3)b, ($\sqrt{b^{2}/3+ℓ^{2}/9}$)/2),
 * ±(±1/2, –($\sqrt{3}$/6)b, ($\sqrt{ℓ^{2}–b^{2}/3}$)/2).