Square-antitegmatic hecatontetracontatetrachoron

Square-antitegmatic hecatontetracontatetrachoron
Rank	4
Type	Uniform dual
Space	Spherical
Notation
Coxeter diagram	m3o4o3m
Elements
Cells	144 square antitegums
Faces	576 kites
Edges	288+384
Vertices	48+192
Vertex figure	192 triangular bipyramids, 48 cubes
Measures (edge length 1)
Dichoral angle	$\arccos\left(-\frac{2+\sqrt2}4\right) ≈ 148.60029°$
Central density	1
Related polytopes
Dual	Small prismatotetracontoctachoron
Abstract properties
Euler characteristic	0
Topological properties
Orientable	Yes
Properties
Symmetry	F4×2, order 2304
Convex	Yes
Nature	Tame

The square-antitegmatic hecatontetracontatetrachoron is a convex isochoric polychoron with 144 square antitegums as cells. It can be obtained as the dual of the small prismatotetracontoctachoron.

It can also be constructed as the convex hull of 2 dual icositetrachora and 2 opposite rectified icositetrachora. If the icositetrachora have edge length 1, the rectified icositetrachora have edge length $2-\sqrt2 ≈ 0.58569$.

Isogonal derivatives

Substitution by vertices of these following elements will produce these convex isogonal polychora:

• Square antitegum (144): Small prismatotetracontoctachoron
• Kite (576): Rectified small prismatotetracontoctachoron
• Edge (288): Tetracontoctachoron
• Edge (384): Bitruncatotetracontoctachoron
• Vertex (48): Bitetracontoctachoron
• Vertex (192): Biambotetracontoctachoron