Triangular-pyritohedral icosahedral duoantiprism

The triangular-pyritohedral icosahedral duoantiprism is a convex isogonal polyteron that consists of 6 pyritohedral icosahedral antiprisms, 8 triangular-triangular duoantiprisms, 6 digonal-triangular duoantiprisms and 72 digonal disphenoidal pyramids obtained through the process of alternating the hexagonal-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:$$\frac{\sqrt6}{2}$$ ≈ 1:1.22474.

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