Triangular antiprism

The triangular antiprism, or trap, 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.

Any such triangular antiprism has an equatorial rectangle section with edges of the same lengths as the antiprism.

Normally the bases of a triangular antiprism are totated by 60° with respect to each other, but if the rotation angle is differne t a chiral version of the triangular antiprism is formed.

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:


 * $$±\left(0,\,\frac{\sqrt3b}{3},\,\sqrt{\frac{12l^2-4b^2}{12}}\right),$$
 * $$±\left(±\frac{b}{2},\,-\frac{\sqrt3b}{6},\,\sqrt{\frac{12l^2-4b^2}{12}}\right),$$