Great deltoidal icositetrahedron

The great deltoidal icositetrahedron is a uniform dual polyhedron. It consists of 24 darts.

If its dual, the quasirhombicuboctahedron, has an edge length of 1, then the short edges of the darts will measure $$2\frac{\sqrt{10+\sqrt2}}{7} ≈ 0.96528$$, and the long edges will be $$\sqrt{2\left(2+\sqrt2\right)} ≈ 2.61313$$. ​The dart faces will have length $$2\frac{\sqrt{31+8\sqrt2}}{7} ≈ 1.85854$$ and width $$\sqrt2 ≈ 1.41421$$. ​The darts have three interior angles of $$\arccos\left(\frac12+\frac{\sqrt2}{4}\right) ≈ 31.39971°$$, and one of $$360°-\arccos\left(-\frac14+\frac{\sqrt2}{8}\right) ≈ 265.80086°$$.

Vertex coordinates
A great deltoidal icositetrahedron with dual edge length 1 has vertex coordinates given by all permutations of:
 * $$\left(±\sqrt2,\,0,\,0\right),$$
 * $$\left(±1,\,±1,\,0\right),$$
 * $$\left(±\frac{4-\sqrt2}{7},\,±\frac{4-\sqrt2}{7},\,±\frac{4-\sqrt2}{7}\right).$$