Digonal-pyritohedral icosahedral duoantiprism

The digonal-pyritohedral icosahedral duoantiprism, or dipidap, is a convex isogonal polyteron that consists of 4 pyritohedral icosahedral antiprisms, 8 digonal-triangular duoantiprisms, 6 digonal-digonal duoantiprisms, and 48 digonal disphenoidal pyramids. 2 pyritohedral icosahedral antiprisms, 2 digonal-triangular duoantiprisms, nd 1 digonal-digonal duoantiprism join at each vertex. It can be obtained through the process of alternating the square-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:$$\frac{\sqrt{34+2\sqrt{37}}}{6}$$ ≈ 1:1.13242.

Vertex coordinates
The vertices of a digonal-pyritohedral icosahedral duoantiprism, assuming that the edge length differences are minimized using the absolute-value method, 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.
 * $$\left(0,\,±\frac12,\,±\frac{1+\sqrt5}{4},\,0,\,±\frac12\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{1+\sqrt5}{4},\,±\frac12,\,0\right),$$

An alternate set of coordinates, assuming that the edge length differences are minimized using the ratio method, 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.
 * $$\left(0,\,±\frac{\sqrt{234-14\sqrt{37}}}{28},\,±\frac{\sqrt{266+42\sqrt{37}}}{28},\,0,\,±\frac12\right),$$
 * $$\left(0,\,±\frac{\sqrt{234-14\sqrt{37}}}{28},\,±\frac{\sqrt{266+42\sqrt{37}}}{28},\,±\frac12,\,0\right),$$