Small sphenoidal heptachiliadiacosichoron

Small sphenoidal heptachiliadiacosichoron
(OFF file)
Rank	4
Type	Uniform dual
Notation
Coxeter diagram	o5m3m3m ()
Elements
Cells	7200 sphenoids
Faces	3600+3600 isosceles triangles, 7200 scalene triangles
Edges	1200+1440+2400+3600
Vertices	120+600+720
Vertex figure	720 pentagonal bipyramids, 600 tetrakis hexahedra, 120 pentakis dodecahedra
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Great rhombated hexacosichoron
Abstract & topological properties
Flag count	172800
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	Yes
Nature	Tame

The small sphenoidal heptachiliadiacosichoron is a convex isochoric polychoron with 7200 sphenoids as cells. It can be obtained as the dual of the great rhombated hexacosichoron.

It can also be constructed as the convex hull of a hecatonicosachoron, a hexacosichoron, and a rectified hexacosichoron. If the hecatonicosachoron has edge length 1, the hexacosichoron has edge length ${\frac {5+3{\sqrt {5}}}{5}}\approx 2.34164$ and the rectified hexacosichoron has edge length $3{\frac {19+13{\sqrt {5}}}{121}}\approx 1.19179$.