Hexagonal-pyritohedral icosahedral duoantiprism

The hexagonal-pyritohedral icosahedral duoantiprism is a convex isogonal polyteron that consists of 12 pyritohedral icosahedral antiprisms, 8 triangular-hexagonal duoantiprisms, 6 digonal-hexagonal duoantiprisms and 144 digonal disphenoidal pyramids obtained through the process of alternating the dodecagonal-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:$\sqrt{462+198√3}$/22 ≈ 1:1.28962.

Vertex coordinates
The vertices of a hexagonal-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, ±1),
 * (0, ±$\sqrt{6}$/6, ±$\sqrt{6}$/3, ±$\sqrt{3}$/2, ±1/2),
 * (0, ±$\sqrt{6}$/6, ±$\sqrt{6}$/3, ±1, 0),
 * (0, ±$\sqrt{6}$/6, ±$\sqrt{6}$/3, ±1/2, ±$\sqrt{3}$/2),