Deltopyramidal hecatonenneacontadichoron

Deltopyramidal hecatonenneacontadichoron
(OFF file)
Rank	4
Type	Uniform dual
Space	Spherical
Notation
Coxeter diagram	m4o3m3m ()
Elements
Cells	192 kite pyramids
Faces	192+192 scalene triangles, 96 kites
Edges	48+64+64+96+96
Vertices	8+16+24+32
Vertex figure	24 octahedra, 32 hexagonal bipyramids, 16 triakis tetrahedra, 8 deltoidal icositetrahedra
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Prismatorhombated tesseract
Abstract & topological properties
Flag count	6144
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B4, order 384
Convex	Yes
Nature	Tame

The rhombipyramidal hecatonenneacontadichoron is a convex isochoric polychoron with 192 kite pyramids as cells. It can be obtained as the dual of the prismatorhombated tesseract.

It can also be constructed as the convex hull of a tesseract, a hexadecachoron, an icositetrachoron (as a rectified hexadecachoron), and a rectified tesseract. If the tesseract has edge length 1, the hexadecachoron has edge length $\frac{5+4\sqrt2}{7} \approx 1.52241$, the icositetrachoron has edge length $\frac{6+5\sqrt2}{14} \approx 0.93365$, and the rectified tesseract has edge length $\frac{1+\sqrt2}{3} \approx 0.80474$.