Tetragonal disphenoid

The tetragonal disphenoid is a type of tetrahedron with four identical isosceles triangles for faces. It can also be considered a digonal antiprism. Tetragonal disphenoids are related to rhombic disphenoids.

The general tetragonal disphenoid can be obtained as the alternation of a square prism. If the tetragonal disphenoid's base edges are of length b and its sides edges are of length l, the corresponding square prism has base edge length $$\frac{b}{\sqrt2}$$ and side edge length $$\sqrt{l^2-\frac{b^2}{2}}$$.

Vertex coordinates
The vertices of a tetragonal disphenoid with base edges of length b and side edges of length l are given by all even permutations of:


 * $$\left(\frac{b\sqrt2}{4},\,\frac{b\sqrt2}{4},\,\frac{\sqrt{l^2-\frac{b^2}{2}}}{2}\right).$$