Tetradyakis hexahedron

The tetradyakis hexahedron is a uniform dual polyhedron. It consists of 48 scalene triangles.

If its dual, the cuboctatruncated cuboctahedron, has an edge length of 1, then the short edges of the triangles will measure $$2\left(\sqrt6-\sqrt3\right) ≈ 1.43488$$, the medium edges will be $$3\sqrt6 ≈ 7.34847$$, and the long edges will be $$2\left(\sqrt6+\sqrt3\right) ≈ 8.36308$$. The triangles have one interior angle of $$\arccos\left(\frac34\right) ≈ 41.40962^\circ$$, one of $$\arccos\left(\frac16+\frac{7\sqrt2}{12}\right) ≈ 7.42069^\circ$$, and one of $$\arccos\left(\frac16-\frac{7\sqrt2}{12}\right) ≈ 131.16968^\circ$$.

Vertex coordinates
A tetradyakis hexahedron with dual edge length 1 has vertex coordinates given by all permutations of:
 * $$\left(±3\left(\sqrt2+1\right),\,0,\,0\right),$$
 * $$\left(±3\left(\sqrt2-1\right),\,0,\,0\right),$$
 * $$\left(±1,\,±1,\,±1\right).$$