Sphenoidal hexecontachoron

Sphenoidal hexecontachoron
(OFF file)
Rank	4
Type	Uniform dual
Notation
Coxeter diagram	m3m3m3o ()
Elements
Cells	60 sphenoids
Faces	30+30 isosceles triangles, 60 scalene triangles
Edges	10+20+20+30
Vertices	5+5+10
Vertex figure	10 triangular bipyramids, 5 triakis tetrahedra, 5 tetrakis hexahedra
Measures (edge length 1)
Dichoral angle	$\arccos \left(-{\frac {29}{34}}\right)\approx 148.53302^{\circ }$
Central density	1
Related polytopes
Dual	Great rhombated pentachoron
Abstract & topological properties
Flag count	1440
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	A4, order 120
Convex	Yes
Nature	Tame

The sphenoidal hexecontachoron is a convex isochoric polychoron with 60 sphenoids as cells. It can be obtained as the dual of the great rhombated pentachoron.

It can also be constructed as the convex hull of 2 dual pentachora and a rectified pentachoron. If the smaller pentachoron has edge length 1, the larger pentachoron has edge length ${\frac {3}{2}}=1.5$ and the rectified pentachoron has edge length ${\frac {9}{13}}\approx 0.69231$.