Hecatonicosadiminished hecatonicosachoron

The hecatonicosadiminished hecatonicosachoron or hidhi is a convex isogonal polychoron that consists of 120 propello tetrahedra and 120 tetrahedra. However, it cannot be made scaliform.

It can be constructed by removing an inscribed hexacosichoron of edge length $$\sqrt{3+\sqrt5}$$ from a hecatonicosachoron.

The ratio between the longest and shortest edges is 1:$$\frac{1+\sqrt5}{2}$$ ≈ 1:1.61803.

Vertex coordinates
Vertex coordinates for a hecatonicosadiminished hecatonicosachoron, created from the vertices of a hecatonicosachoron of edge length 1, are given by all even permutations and all sign changes of: as well as all permutations and even sign changes of: as well as all permutations and odd sign changes of:
 * $$\left(\frac{7+3\sqrt{5}}{4},\,\frac{3+\sqrt{5}}{4},\,\frac{1}{2},\,0\right),$$
 * $$\left(\frac{2+\sqrt{5}}{2},\,\frac{5+3\sqrt{5}}{4},\,0,\,\frac{1+\sqrt{5}}{4}\right),$$
 * $$\left(\frac{2+\sqrt{5}}{2},\,\frac{3+\sqrt{5}}{4},\,\frac{3+\sqrt{5}}{2},\,\frac{1+\sqrt{5}}{4}\right),$$
 * $$\left(\frac{2+\sqrt{5}}{2},\,\frac{2+\sqrt{5}}{2},\,\frac{2+\sqrt{5}}{2},\,\frac{1}{2}\right),$$
 * $$\left(\frac{7+3\sqrt{5}}{4},\,\frac{1+\sqrt{5}}{4},\,\frac{1+\sqrt{5}}{4},\,\frac{1+\sqrt{5}}{4}\right),$$
 * $$\left(\frac{5+3\sqrt{5}}{4},\,\frac{3+\sqrt{5}}{4},\,\frac{3+\sqrt{5}}{4},\,\frac{3+\sqrt{5}}{4}\right).$$