Tri-hecatonicosadiminished hecatonicosachoron

Tri-hecatonicosadiminished hecatonicosachoron
File:Tri-hecatonicosadiminished hecatonicosachoron.png (OFF file)
Rank	4
Type	Isogonal
Notation
Bowers style acronym	Thidhi
Elements
Cells	360 phyllic disphenoids, 360 digonal disphenoids, 120 chiral gyroelongated triangular tegums
Faces	720+720+720 isosceles triangles
Edges	120+360+360+720
Vertices	240
Vertex figure	13-vertex polyhedron with 3 pentagons and 13 triangles
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Tri-hecatonicosastellated hexacosichoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H3●G2, order 720
Convex	Yes
Nature	Tame

The tri-hecatonicosadiminished hecatonicosachoron or thidhi is a convex isogonal polychoron that consists of 120 chiral gyroelongated triangular tegums, 360 digonal disphenoids, and 360 phyllic disphenoids. 4 chiral gyroelongaed triangular tegums, 6 phyllic disphenoids, and 6 digonal disphenoids join at each vertex. However, it cannot be made scaliform.

It can be constructed by removing three inscribed hexacosichora of edge length ${\sqrt {3+{\sqrt {5}}}}$ from a hecatonicosachoron.

The ratio between the longest and shortest edges is 1:${\frac {{\sqrt {2}}+{\sqrt {10}}}{2}}$ ≈ 1:2.28825.