Pyritohedral icosahedral duoantiprism

The pyritohedral icosahedral duoantiprism, or pikdap, is a convex isogonal polypeton that consists of 16 triangular-pyritohedral icosahedral duoantiprisms, 12 digonal-pyritohedral icosahedral duoantiprisms, and 288 isosceles triangular disphenoids. 4 triangular-pyritohedral icosahedral duoantiprisms, 2 digonal-pyritohedral icosahedral duoantiprisms, and 6 isosceles triangular disphenoids join at each vertex. It can be obtained through the process of alternating the truncated octahedral duoprism. 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 pyritohedral icosahedral duoantiprism, assuming that the edge length differences are minimized, centered at the origin, are given by all sign changes and all even permutations of two sets of three coordinates (a, b, c) and (d, e, f) of:
 * $$\left(0,\,±\frac12,\,±1,\,0,\,±\frac12,\,±1\right),$$
 * $$\left(0,\,±1,\,±\frac12,\,0,\,±1,\,±\frac12\right).$$