Disdyakis triacontahedral tegum

Disdyakis triacontahedral tegum
Rank	4
Type	Uniform dual
Space	Spherical
Notation
Coxeter diagram	m2m5m3m
Elements
Cells	240 irregular tetrahedra
Faces	120+120+120+120 scalene triangles
Edges	24+40+60+60+60+60
Vertices	2+12+20+30
Vertex figure	2 disdyakis triacontahedra, 12 decagonal tegums, 20 hexagonal tegums, 30 octahedra
Measures (edge length 1)
Dichoral angle	$\arccos\left(-\frac{30+3\sqrt5}{38}\right) ≈ 165.01762°$
Central density	1
Related polytopes
Dual	Great rhombicosidodecahedral prism
Conjugate	Great disdyakis triacontahedral tegum
Abstract properties
Euler characteristic	0
Topological properties
Orientable	Yes
Properties
Symmetry	H3×A1, order 240
Convex	Yes
Nature	Tame

The disdyakis triacontahedral tegum, also called the disdyakis triacontahedral bipyramid, is a convex isochoric polychoron with 240 irregular tetrahedra as cells. As the name suggests, it can be constructed as a tegum based on the disdyakis triacontahedron.

In the variant obtained as the dual of the uniform great rhombicosidodecahedral prism, if the shortest edges of the disdyakis triacontahedron have length 1, its height is $\sqrt{\frac{4155+1857\sqrt5}{5}} ≈ 40.76120$.