Deltopyramidal pentacosiheptacontahexachoron

Deltopyramidal pentacosiheptacontahexachoron
Rank	4
Type	Uniform dual
Space	Spherical
Notation
Coxeter diagram	m3m4o3m
Elements
Cells	576 kite pyramids
Faces	576+576 scalene triangles, 288 kites
Edges	144+192+192+288+288
Vertices	24+24+96+96
Vertex figure	96 triangular bipyramids, 96 hexagonal bipyramids, 24 tetrakis hexahedra, 24 deltoidal icositetrahedra
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Prismatorhombated icositetrachoron
Abstract properties
Euler characteristic	0
Topological properties
Orientable	Yes
Properties
Symmetry	F4, order 1152
Convex	Yes
Nature	Tame

The deltopyramidal pentacosiheptacontahexachoron is a convex isochoric polychoron with 576 kite pyramids as cells.

It can also be constructed as the convex hull of 2 dual icositetrachora and 2 opposite rectified icositetrachora. If the smaller icositetrachoron has edge length 1, the larger icositetrachoron has edge length $11-7\sqrt2 ≈ 1.10051$, the smaller rectified icositetrachoron has edge length $\frac{41-\sqrt2}{73} ≈ 0.54227$, and the larger rectified icositetrachoron has edge length $\frac{9\sqrt2-1}{21} ≈ 0.55847$.