Rhombipyramidal hexecontachoron

Rhombipyramidal hexecontachoron
(OFF file)
Rank	4
Type	Uniform dual
Notation
Coxeter diagram	m3m3o3m ()
Elements
Cells	60 skew rhombic pyramids
Faces	60+60 scalene triangles, 30 rhombi
Edges	20+20+20+30+30
Vertices	5+5+10+10
Vertex figure	10 triangular bipyramids, 10 hexagonal bipyramids, 5 triakis tetrahedra, 5 rhombic dodecahedra
Measures (edge length 1)
Dichoral angle	$\arccos \left(-{\frac {21}{26}}\right)\approx 143.87107^{\circ }$
Central density	1
Related polytopes
Dual	Prismatorhombated pentachoron
Abstract & topological properties
Flag count	1920
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	A4, order 120
Convex	Yes
Nature	Tame

The rhombipyramidal hexecontachoron is a convex isochoric polychoron with 60 skew rhombic pyramids as cells. It can be obtained as the dual of the prismatorhombated pentachoron.

It can also be constructed as the convex hull of 2 dual pentachora and 2 opposite rectified pentachora. If the smaller pentachoron has edge length 1, the larger pentachoron has edge length ${\frac {8}{7}}\approx 1.14286$, the smaller rectified pentachoron has edge length ${\frac {8}{11}}\approx 0.72727$, and the larger rectified pentachoron has edge length ${\frac {8}{9}}\approx 0.88889$.