Deltoidal hexecontahedral tegum

Deltoidal hexecontahedral tegum
Rank	4
Type	Uniform dual
Space	Spherical
Notation
Coxeter diagram	m2m5o3m
Elements
Cells	120 kite pyramids
Faces	120+120 scalene triangles, 60 kites
Edges	24+40+60+60+60+60
Vertices	2+12+20+30
Vertex figure	2 edltoidal hexecontahedra, 12 pentagonal tegums, 20 triangular tegums, 30 octahedra
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Small rhombicosidodecahedral prism
Conjugate	Great deltoidal hexecontahedral tegum
Abstract properties
Euler characteristic	0
Topological properties
Orientable	Yes
Properties
Symmetry	H3×A1, order 240
Convex	Yes
Nature	Tame

The deltoidal hexecontahedral tegum, also called the deltoidal hexecontahedral bipyramid, is a convex isochoric polychoron with 120 kite pyramids as cells. As the name suggests, it can be constructed as a tegum based on the deltoidal hexecontahedron.

In the variant obtained as the dua; of the uniform small rhombicosidodecahedral prism, if the short edges of the deltoidal hexecontahedron have length 1, its height is $\sqrt{\frac{1385+619\sqrt5}{5}} ≈ 23.53349$.