Pentagonal-pyritohedral icosahedral duoantiprism

The pentagonal-pyritohedral icosahedral duoantiprism is a convex isogonal polyteron that consists of 10 pyritohedral icosahedral antiprisms, 8 triangular-pentagonal duoantiprisms, 6 digonal-pentagonal duoantiprisms and 120 digonal disphenoidal pyramids obtained through the process of alternating the decagonal-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:$$\sqrt{\frac{75+9\sqrt5}{58}}$$ ≈ 1:1.28066.

Vertex coordinates
The vertices of a pentagonal-pyritohedral icosahedral duoantiprism, assuming that the edge length differences are minimized, 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, ±$\sqrt{6}$/6, ±$\sqrt{6}$/3, 0, $\sqrt{50+10√5}$/10),
 * (0, ±$\sqrt{6}$/6, ±$\sqrt{6}$/3, ±(1+$\sqrt{5}$)/4, $\sqrt{50–10√5}$/20),
 * (0, ±$\sqrt{6}$/6, ±$\sqrt{6}$/3, ±1/2, –$\sqrt{25+10√5}$/10),
 * (0, ±$\sqrt{6}$/6, ±$\sqrt{6}$/3, 0, -$\sqrt{50+10√5}$/10),
 * (0, ±$\sqrt{6}$/6, ±$\sqrt{6}$/3, ±(1+$\sqrt{5}$)/4, -$\sqrt{50–10√5}$/20),
 * (0, ±$\sqrt{6}$/6, ±$\sqrt{6}$/3, ±1/2, $\sqrt{25+10√5}$/10),