Joined hecatonicosachoron

The joined hexacosichoron, also known as the pentagonal-bipyramidal heptacosicosachoron or pibhaki, is a convex isochoric polychoron with 720 pentagonal tegums 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 $$\frac{5+3\sqrt5}{5} ≈ 2.34164$$ 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