Sphenoidal hecatonenneacontadichoron

Sphenoidal hecatonenneacontadichoron
(OFF file)
Rank	4
Type	Uniform dual
Notation
Coxeter diagram	m4m3m3o ()
Elements
Cells	192 sphenoids
Faces	96+96 isosceles triangles, 192 scalene triangles
Edges	24+64+64+96
Vertices	8+16+32
Vertex figure	32 triangular bipyramids, 16 triakis tetrahedra, 8 disdyakis dodecahedra
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Great rhombated tesseract
Abstract & topological properties
Flag count	4608
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B4, order 384
Convex	Yes
Nature	Tame

The sphenoidal hecatonicenneacontadichoron is a convex isochoric polychoron with 192 sphenoids as cells. It can be obtained as the dual of the great rhombated tesseract.

It can also be constructed as the convex hull of a tesseract, a hexadecachoron, and a rectified tesseract. If the tesseract has edge length 1, the hexadecachoron has edge length ${\frac {3+8{\sqrt {2}}}{7}}\approx 2.04482$ and the rectified tesseract has edge length ${\frac {5+19{\sqrt {2}}}{41}}\approx 0.77732$.