Disphenoidal chiliahecatonpentacontadichoron

Disphenoidal chiliahecatonpentacontadichoron
(OFF file)
Rank	4
Type	Uniform dual
Notation
Coxeter diagram	m3m4m3m ()
Elements
Cells	1152 phyllic disphenoids
Faces	1152+1152 scalene triangles
Edges	144+288+384+576
Vertices	48+192
Vertex figure	192 hexagonal bipyramids, 48 disdyakis dodecahedra
Measures (edge length 1)
Dichoral angle	$\arccos \left(-{\frac {54+9{\sqrt {2}}}{68}}\right)\approx 168.90009^{\circ }$
Central density	1
Related polytopes
Dual	Great prismatotetracontoctachoron
Abstract & topological properties
Flag count	27648
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	F4×2, order 2304
Convex	Yes
Nature	Tame

The disphenoidal chiliahecatonpentacontadichoron is a convex isochoric polychoron with 1152 phyllic disphenoids as cells. It can be obtained as the dual of the great prismatotetracontoctachoron.

It can also be constructed as the convex hull of 2 dual icositetrachora and 2 opposite rectified icositetrachora. If the icositetrachora have edge length 1, the rectified icositetrachora have edge length ${\frac {3-{\sqrt {2}}}{3}}\approx 0.52860$.