Tetrakis hexacosichoron

Tetrakis hexacosichoron
(OFF file)
Rank	4
Type	Uniform dual
Notation
Coxeter diagram	m5m3o3o ()
Elements
Cells	2400 triangular pyramids
Faces	1200 triangles, 3600 isosceles triangles
Edges	720+2400
Vertices	120+600
Vertex figure	600 tetrahedra, 120 triakis icosahedra
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Truncated hecatonicosachoron
Abstract & topological properties
Flag count	57600
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	Yes
Nature	Tame

The tetrakis hexacosichoron, also known as the triangular-pyramidal dischilliatetracosichoron, is a convex isochoric polychoron with 2400 triangular pyramids as cells. It can be obtained as the dual of the truncated hecatonicosachoron.

It can also be obtained as the convex hull of a hecatonicosachoron and a hexacosichoron, where the edges of the hexacosichoron are ${\frac {10+{\sqrt {5}}}{5}}\approx 2.44721$ times the length of those of the hecatonicosachoron. Varying the hexacosichoron's edge length to be anything more than $3{\frac {1+{\sqrt {5}}}{4}}\approx 2.42705$ times that of the hecatonicosachoron gives a fully symmetric variant of this polychoron.