Joined hecatonicosachoron

The joined hexacosichoron, also known as the isochoric polychoron with 720 pentagonal bipyramids as cells. It can be obtained as the dual of the rectified hexacosichoron.

It can also be obtained as the convex hull of a hecatonicosachoron and a hexacosichoron, where the edges of the hexacosichoron are $$\frac{5+3\sqrt5}{5}$$ times the length of those of the hecatonicosachoron.

The ratio between the longest and shortest edges is 1:$$\frac{5+\sqrt5}{5}$$ ≈ 1:1.44721. Each face is an isosceles triangle that uses one short and two long edges.

Isogonal derivatives
Substitution by vertices of these following elements will produce these convex isogonal polychora:
 * Pentagonal bipyramid (720): Rectified hexacosichoron
 * Isosceles triangle (3600): Semi-uniform small rhombated hexacosichoron
 * Edge (1200): Rectified hecatonicosachoron
 * Edge (2400): Semi-uniform small disprismatohexacosihecatonicosachoron
 * Vertex (120): Hexacosichoron
 * Vertex (600): Hecatonicosachoron