Rhombipyramidal hecatonenneacontadichoron

Rhombipyramidal hecatonenneacontadichoron
(OFF file)
Rank	4
Type	Uniform dual
Space	Spherical
Notation
Coxeter diagram	m4m3o3m ()
Elements
Cells	192 rhombic pyramids
Faces	192+192 scalene triangles, 96 rhombi
Edges	48+64+64+96+96
Vertices	8+16+24+32
Vertex figure	32 triangular bipyramids, 24 octagonal bipyramids, 8 triakis octahedra, 16 rhombic dodecahedra
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Prismatorhombated hexadecachoron
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 skew rhombic pyramids as cells. It can be obtained as the dual of the prismatorhombated hexadecachoron.

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 $2\frac{2+3\sqrt2}{7} \approx 1.78361$, the icositetrachoron has edge length $2\frac{1+2\sqrt2}{7} \approx 1.09384$, and the rectified tesseract has edge length $2\frac{2+5\sqrt2}{23} \approx 0.78879$.