Rhombic triacontahedral tegum

Rhombic triacontahedral tegum
Rank	4
Type	Uniform dual
Space	Spherical
Notation
Coxeter diagram	m2o5m3o
Elements
Cells	60 rhombic pyramids
Faces	120 scalene triangles, 30 golden rhombi
Edges	24+40+60
Vertices	2+12+20
Vertex figure	2 rhombic triacontahedra, 12 pentagonal tegums, 20 triangular tegums
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Icosidodecahedral prism
Conjugate	Great rhombic triacontahedral tegum
Abstract properties
Euler characteristic	0
Topological properties
Orientable	Yes
Properties
Symmetry	H3×A1, order 240
Convex	Yes
Nature	Tame

The rhombic triacontahedral tegum, also called the rhombic triacontahedral bipyramid, is a convex isochoric polychoron with 60 rhombic pyramids as cells. As the name suggests, it can be constructed as a tegum based on the rhombic triacontahedron.

In the variant obtained as the dual of the uniform icosidodecahedral prism, the height from the top to the bottom edges is $\sqrt{\frac{200+88\sqrt5}{5}} ≈ 8.90813$ times the edge length of the base rhombic triacontahedron.