Great triakis octahedron

The great triakis octahedron is a uniform dual polyhedron. It consists of 24 isosceles triangles.

If its dual, the quasitruncated hexahedron, has an edge length of 1, then the short edges of the triangles will measure $$2-\sqrt2 ≈ 0.58579$$, and the long edges will have a length of 2. The triangles have two interior angles of $$\arccos\left(\frac12-\frac{\sqrt2}{4}\right) ≈ 81.57894^\circ$$, and one of $$\arccos\left(\frac14+\frac{\sqrt2}{2}\right) ≈ 16.84212^\circ$$.

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