Triangular-pyritohedral icosahedral duoantiprism

The triangular-pyritohedral icosahedral duoantiprism, or trapidap, 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. 2 pyritohedral icosahedral antiprisms, 2 triangular-triangular duoantiprisms, 1 digonal-triangular duoantiprism, and 5 digonal disphenoidal pyramids join at each vertex. It can be 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.
 * $$\left(0,\,±\frac{\sqrt6}{6},\,±\frac{\sqrt6}{3},\,0,\,\frac{\sqrt3}{3}\right),$$
 * $$\left(0,\,±\frac{\sqrt6}{6},\,±\frac{\sqrt6}{3},\,±\frac12,\,-\frac{\sqrt3}{6}\right),$$
 * $$\left(0,\,±\frac{\sqrt6}{6},\,±\frac{\sqrt6}{3},\,0,\,-\frac{\sqrt3}{3}\right),$$
 * $$\left(0,\,±\frac{\sqrt6}{6},\,±\frac{\sqrt6}{3},\,±\frac12,\,\frac{\sqrt3}{6}\right),$$