Digonal-pyritohedral icosahedral duoantiprism

The digonal-pyritohedral icosahedral duoantiprism is a convex isogonal polyteron that consists of 4 pyritohedral icosahedral antiprisms, 8 digonal-triangular duoantiprisms, 6 digonal-digonal duoantiprisms and 48 digonal disphenoidal pyramids obtained through the process of alternating the square-truncated octahedral duoprism. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{\sqrt{34+2\sqrt37}}{6}$$ ≈ 1:1.13242.

Vertex coordinates
The vertices of a digonal-pyritohedral icosahedral duoantiprism, assuming that the edge length differences are minimized using the absolute-value method, centered at the origin, are given by: with all even permutations of the first three coordinates, and with all odd permutations of the first three coordinates.
 * (0, ±1/2, ±(1+$\sqrt{5}$)/4, 0, ±1/2),
 * (0, ±1/2, ±(1+$\sqrt{5}$)/4, ±1/2, 0),

An alternate set of coordinates, assuming that the edge length differences are minimized using the ratio method, centered at the origin, are given by: with all even permutations of the first three coordinates, and with all odd permutations of the first three coordinates.
 * (0, ±$\sqrt{238-14√37}$/28, ±$\sqrt{266+42√37}$/28, 0, ±1/2),
 * (0, ±$\sqrt{238-14√37}$/28, ±$\sqrt{266+42√37}$/28, ±1/2, 0),