Digonal tetrahedroorthowedge

The digonal tetrahedroorthowedge is a convex isogonal polyteron that consists of 8 bilaterally-symmetric pentachora and 4 isosceles triangular duotegums. 3 triangular duotegums and 8 pentachora join at each vertex. It can be formed as a quotient prism based on a compound of four digons. However, it cannot be made uniform. Along with the square disphenoid, it is one of the two known isogonal polytera with 8 vertices.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{\sqrt{4+2\sqrt2}}{2}$$ ≈ 1:1.30656.

Vertex coordinates
Vertex coordinates for a digonal tetrahedroorthowedge, assuming that the edge length differences are minimized, using the ratio method, are given by all even permutations of the first two coordinates of:
 * $$\left(0,\,\frac12,\,\frac{\sqrt{4+2\sqrt2}}{8},\,\frac{\sqrt{4+2\sqrt2}}{8},\,\frac{\sqrt{4+2\sqrt2}}{8}\right),$$
 * $$\left(\frac{\srt2}{4},\,\frac{\srt2}{4},\,\frac{\sqrt{4+2\sqrt2}}{8},\,-\frac{\sqrt{4+2\sqrt2}}{8},\,-\frac{\sqrt{4+2\sqrt2}}{8}\right,$$
 * $$\left(\frac12,\,0,\,-\frac{\sqrt{4+2\sqrt2}}{8},\,-\frac{\sqrt{4+2\sqrt2}}{8},\,\frac{\sqrt{4+2\sqrt2}}{8}\right),$$
 * $$\left(\frac{\sqrt2}{4},\,-\frac{\sqrt2}{4},\,-\frac{\sqrt{4+2\sqrt2}}{8},\,\frac{\sqrt{4+2\sqrt2}}{8},\,-\frac{\sqrt{4+2\sqrt2}}{8}\right).$$