Digonal-square duoantiprism

The digonal-square duoantiprism, also known as the 2-4 duoantiprism, is a convex isogonal polychoron that consists of 4 square antiprisms, 8 tetragonal disphenoids and 16 digonal disphenoids obtained through the process of alternating the square-octagonal duoprism. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$\sqrt{42+14√2}$/7 ≈ 1:1.12303.

Vertex coordinates
The vertices of a digonal–square duoantiprism, assuming that the square antiprisms are uniform of edge length 1, centered at the origin, are given by:
 * (0, ±$\sqrt{2}$/2, $\sqrt{8|4}$/4, $\sqrt{8|4}$/4),
 * (0, ±$\sqrt{2}$/2, –$\sqrt{8|4}$/4, –$\sqrt{8|4}$/4),
 * (±$\sqrt{2}$/2, 0, $\sqrt{8|4}$/4, $\sqrt{8|4}$/4),
 * (±$\sqrt{2}$/2, 0, –$\sqrt{8|4}$/4, –$\sqrt{8|4}$/4),
 * (±1/2, ±1/2, $\sqrt{8|4}$/4, –$\sqrt{8|4}$/4),
 * (±1/2, ±1/2, –$\sqrt{8|4}$/4, $\sqrt{8|4}$/4).

An alternate set of coordinates, assuming that the edge length differences are minimized, centered at the origin, are given by:
 * (0, ±$\sqrt{2}$/2, $\sqrt{2}$/4, $\sqrt{2}$/4),
 * (0, ±$\sqrt{2}$/2, –$\sqrt{2}$/4, –$\sqrt{2}$/4),
 * (±$\sqrt{2}$/2, 0, $\sqrt{2}$/4, $\sqrt{2}$/4),
 * (±$\sqrt{2}$/2, 0, –$\sqrt{2}$/4, –$\sqrt{2}$/4),
 * (±1/2, ±1/2, $\sqrt{2}$/4, –$\sqrt{2}$/4),
 * (±1/2, ±1/2, –$\sqrt{2}$/4, $\sqrt{2}$/4).