Great triakis octahedron

In geometry, the great triakis octahedron is the dual of the stellated truncated hexahedron (U19). It has 24 intersecting isosceles triangle faces. Part of each triangle lies within the solid, hence is invisible in solid models.

Proportions
The triangles have one angle of $$\arccos(\frac{1}{4}+\frac{1}{2}\sqrt{2})\approx 16.842\,116\,236\,30^{\circ}$$ and two of $$\arccos(\frac{1}{2}-\frac{1}{4}\sqrt{2})\approx 81.578\,941\,881\,85^{\circ}$$. The dihedral angle equals $$\arccos(\frac{-3+8\sqrt{2}}{17})\approx 60.722\,386\,809\,64^{\circ}$$.