Digonal-square prismantiprismoid

The digonal-square prismantiprismoid, also known as the edge-snub digonal-square duoprism or 2-4 prismantiprismoid, is a convex isogonal polychoron that consists of 4 rectangular trapezoprisms, 4 tetragonal disphenoids and 8 wedges obtained through the process of edge-alternating the square-octagonal duoprism. However, it cannot be made uniform.

A variant with regular tetrahedra and squares can be vertex-inscribed into a rectified tesseract.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:(1+$\sqrt{3}$)/2 ≈ 1:1.36603.

Vertex coordinates
The vertices of a digonal-square prismantiprismoid, assuming that the tetragonal disphenoids are regular and are connected by squares of edge length 1, centered at the origin, are given by:
 * (0, ±1/2, ±1/2, ±1),
 * (±1/2, 0, ±1, ±1/2).

An alternate set of coordinates, assuming that the edge length differences are minimized, centered at the origin, are given by:
 * (0, ±1/2, ±($\sqrt{3}$-1)/2, ±1/2),
 * (±1/2, 0, ±1/2, ±($\sqrt{3}$-1)/2).