Triangular-antitegmatic dischiliatetracosichoron

Triangular-antitegmatic dischiliatetracosichoron
(OFF file)
Rank	4
Type	Uniform dual
Space	Spherical
Notation
Coxeter diagram	m5o3o3m ()
Elements
Cells	2400 triangular antitegums
Faces	3600+3600 kites
Edges	1440+2400+3600
Vertices	120+600+720+1200
Vertex figure	1200 triangular bipyramids, 720 pentagonal bipyramids, 600 tetrahedra, 120 icosahedra
Measures (edge length 1)
Dichoral angle	$\arccos\left(-\frac{9+3\sqrt5}{16}\right) \approx 169.04078^\circ$
Central density	1
Related polytopes
Dual	Small disprismatohexacosihecatonicosachoron
Abstract & topological properties
Flag count	115200
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	Yes
Nature	Tame

The triangular-antitegmatic dischiliatetracosichoron is a convex isochoric polychoron with 2400 triangular antitegums as cells. It can be obtained as the dual of the small disprismatohexacosihecatonicosachoron.

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 $\frac{17+4\sqrt5}{11} \approx 2.35857$, the rectified hexacosichoron has edge length $\frac{29-\sqrt5}{22} \approx 1.21654$, and the rectified hecatonicosachoron has edge length $12-5\sqrt5 \approx 0.81966$.