Sphenoidal pentacosiheptacontahexachoron

Sphenoidal pentacosiheptacontahexachoron
Rank	4
Type	Uniform dual
Space	Spherical
Notation
Coxeter diagram	m3m4m3o
Elements
Cells	576 sphenoids
Faces	288+288 isosceles triangles, 576 scalene triangles
Edges	96+144+192+288
Vertices	24+24+96
Vertex figure	96 triangular bipyramids, 24 triakis octahedra, disdyakis dodecahedra
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Great rhombated icositetrachoron
Abstract properties
Euler characteristic	0
Topological properties
Orientable	Yes
Properties
Symmetry	F4, order 1152
Convex	Yes
Nature	Tame

The sphenoidal pentacosiheptacontahexachoron is a convex isochoric polychoron with 576 sphenoids as cells. It can be obtained as the dual of the great rhombated icositetrachoron.

It can also be constructed as the convex hull of 2 dual icositetrachora and a rectified icositetrachoron. If the smaller icositetrachoron has edge length 1, the larger icositetrachoron has edge length $\frac{3\sqrt2-1}{2} ≈ 1.08088$ and the rectified icositetrachoron has edge length $\frac{29-2\sqrt2}{49} ≈ 0.53411$.