Rhombipyramidal heptachiliadiacosichoron

Rhombipyramidal heptachiliadiacosichoron
(OFF file)
Rank	4
Type	Uniform dual
Notation
Coxeter diagram	m5m3o3m ()
Elements
Cells	7200 skew rhombic pyramids
Faces	7200+7200 scalene triangles, 3600 rhombi
Edges	1440+2400+2400+3600+3600
Vertices	120+600+720+1200
Vertex figure	1200 triangular bipyramids 720 decagonal bipyramids, 120 triakis icosahedra, 600 rhombic dodecahedra
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Prismatorhombated hexacosichoron
Abstract & topological properties
Flag count	230400
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	Yes
Nature	Tame

The rhombipyramidal heptachiliadiacosichoron is a convex isochoric polychoron with 7200 skew rhombic pyramids as cells.

It can also be constructed as the convex hull of a hecatonicosachoron, a hexacosichoron, a rectified hexacosichoron, and a rectified hecatonicosachoron. If the hecatonicosachoron has edge length 1, the hexacosichoron has edge length $2{\frac {19+7{\sqrt {5}}}{29}}\approx 2.38983$, the rectified hexacosichoron has edge length $4{\frac {10+3{\sqrt {5}}}{55}}\approx 1.21514$, and the rectified hecatonicosachoron has edge length $2{\frac {21+5{\sqrt {5}}}{79}}\approx 0.81469$.