Digonal-square prismantiprismoid

The digonal-square prismantiprismoid or dispap, 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. 1 tetrgonal disphenoid, 2 rectangular trapezoprisms, and 3 wedges join at each vertex. It can be obtained through the process of alternating one class of edges of the square-octagonal duoprism so that the octagons become rectangles. However, it cannot be made uniform, as it generally has 4 edge lengths, which can be minimized to no fewer than 2 different sizes.

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:$$\frac{1+\sqrt3}{2}$$ ≈ 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:
 * $$\left(0,\,±\frac12,\,±\frac12,\,±1\right),$$
 * $$\left(±\frac12,\,0,\,±1,\,±\frac12\right).$$

An alternate set of coordinates, assuming that the edge length differences are minimized, centered at the origin, are given by:
 * $$\left(0,\,±\frac12,\,±\frac{\sqrt3-1}{2},\,±\frac12\right),$$
 * $$\left(±\frac12,\,0,\,±\frac12,\,±\frac{\sqrt3-1}{2}\right).$$

An additional variant based on a unit square-octagonal duoprism has vertices given by:
 * $$\left(0,\,±\frac{\sqrt2}{2},\,±\frac12,\,±\frac{1+\sqrt2}{2}\right),$$
 * $$\left(±\frac{\sqrt2}{2},\,0,\,±\frac{1+\sqrt2}{2},\,±\frac12\right).$$