Tri-icositetradiminished hexacosichoron

Tri-icositetradiminished hexacosichoron
(OFF file)
Rank	4
Type	Noble
Space	Spherical
Notation
Bowers style acronym	Tridex
Elements
Cells	72 bi-tridiminished icosahedra
Faces	144 isosceles triangles, 72 isosceles trapezoids
Edges	48+72+72
Vertices	48
Vertex figure	Tri-tridiminished icosahedron
Measures (as derived from unit hexacosichoron)
Edge lengths	Short edges (72): 1
	Long edges (48+72): $\frac{1+\sqrt5}{2} ≈ 1.61803$
Circumradius	$\frac{1+\sqrt5}{2} ≈ 1.61803$
Central density	1
Related polytopes
Army	Tridex
Regiment	Tridex
Dual	Bi-icositetradiminished hexacosichoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	(B3/2)●G2, order 144
Convex	Yes
Nature	Tame

The tri-icositetradiminished hexacosichoron or tridex, also known as the tetragonal-antiwedge heptacontadichoron or tetragonal-antiwedge hexafold pyritocubiswirlchoron, is a noble polychoron with 72 bi-tridiminished icosahedra as cells. 9 cells join at each vertex. It can be obtained by diminishing the vertices of three icositetrachora from the hexacosichoron, and is the dual of the bi-icositetradiminished hexacosichoron.

The ratio between the longest and shortest edges is 1:$\frac{1+\sqrt5}{2}$ ≈ 1:1.61803.

External links

• Wikipedia Contributors. "Tri-24-diminished 600-cell".
• Klitzing, Richard. "tridex".