Triakis icosahedral tegum

Triakis icosahedral tegum
Rank	4
Type	Uniform dual
Space	Spherical
Notation
Coxeter diagram	m2m5m3o
Elements
Cells	120 sphenoids
Faces	60+60 isosceles triangles, 120 scalene triangles
Edges	24+30+40+60
Vertices	2+12+20
Vertex figure	2 triakis icosahedra, 12 decagonal tegums, 20 triangular tegums
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Truncated dodecahedral prism
Conjugate	Great triakis icosahedral tegum
Abstract properties
Euler characteristic	0
Topological properties
Orientable	Yes
Properties
Symmetry	H3×A1, order 240
Convex	Yes
Nature	Tame

The triakis icosahedral tegum, also known as the triakis icosahedral bipyramid, is a convex isochoric polychoron with 120 sphenoids as cells. As the name suggests, it can be constructed as a tegum based on the triakis icosahedron.

In the variant obtained as the dual of the uniform truncated dodecahedral prism, if the short edges of the triakis icosahedron have length 1, its height is $\frac{17+7\sqrt5}{2} ≈ 16.32624$.