Dodecakis hecatonicosachoron

The dodecakis hecatonicosachoron, also known as the pentagonal-pyramidal chilliatetracositetracontachoron, is a convex isochoric polychoron with 1440 pentagonal pyramids as cells. It can be constructed as the dual of the truncated hexacosichoron.

It can also be obtained as the convex hull of a hecatonicosachoron and a hexacosichoron, where the edges of the hexacosichoron are $$3\frac{13+7\sqrt5}{38} ≈ 2.26204$$ times the length of those of the hecatonicosachoron. Varying the hexacosichoron's edge length to be anything less than $$\frac{5+3\sqrt5}{5} ≈ 2.34164$$ times that of the hecatonicosachoron gives a fully symmetric variant of this polychoron.