Pentakis dodecahedral tegum

Pentakis dodecahedral tegum
Rank	4
Type	Isochoric
Space	Spherical
Notation
Coxeter diagram	m2o5m3m
Elements
Cells	120 sphenoids
Faces	60+60 isosceles triangles, 120 scalene triangles
Edges	24+30+40+60
Vertices	2+12+20
Vertex figure	2 pentakis dodecahedra, 20 hexagonal tegums, 12 pentagonal tegums
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Truncated icosahedral prism
Conjugate	Great stellapentakis dodecahedral tegum
Abstract properties
Euler characteristic	0
Topological properties
Orientable	Yes
Properties
Symmetry	H3×A1, order 240
Convex	Yes
Nature	Tame

The pentakis dodecahedral tegum, also called the pentakis dodecahedral 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 pentakis dodecahedron.

In the variant obtained as the dual of the uniform truncated icosahedral prism, if the short edges of the pentakis dodecahedron have length 1, its height is $\frac{1+7\sqrt2}{2} ≈ 14.32624$.