Great rhombihexacron

The great rhombihexacron is a uniform dual polyhedron. It consists of 24 butterflies.

If its dual, the great rhombihexahedron, has an edge length of 1, then the short edges of the bowties will measure $$\sqrt{2\left(2-\sqrt2\right)} ≈ 1.08239$$, and the long edges will be $$2\sqrt{2-\sqrt2} ≈ 1.53073$$. The butterflies have two interior angles of $$\arccos\left(\frac12+\frac{\sqrt2}{4}\right) ≈ 31.39971°$$, and two of $$\arccos\left(-\frac14+\frac{\sqrt2}{2}\right) ≈ 62.79943°$$. The intersection has an angle of $$\arccos\left(\frac14-\frac{\sqrt2}{8}\right) ≈ 85.80086°$$.

Vertex coordinates
A great rhombihexacron with dual edge length 1 has vertex coordinates given by all permutations of:
 * $$\left(±\left(2-\sqrt2\right),\,0,\,0\right),$$
 * $$\left(±1,\,±1,\,0\right).$$