Disphenoidal enneacontahexachoron

Disphenoidal enneacontahexachoron
(OFF file)
Rank	4
Type	Uniform dual
Space	Spherical
Notation
Coxeter diagram	o4m3m3o ()
Elements
Cells	96 digonal disphenoids
Faces	96+96 isosceles triangles
Edges	24+32+64
Vertices	8+16
Vertex figure	16 triakis tetrahedra, 8 tetrakis hexahedra
Measures (edge length 1)
Dichoral angle	$\arccos\left(-\frac89\right) \approx 152.73396^\circ$
Central density	1
Related polytopes
Dual	Tesseractihexadecachoron
Abstract & topological properties
Flag count	2304
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B4, order 384
Convex	Yes
Nature	Tame

The disphenoidal enneacontahexachoron is a convex isochoric polychoron with 96 digonal disphenoids as cells. It can be obtained as the dual of the tesseractihexadecachoron.

It can also be obtained as the convex hull of a tesseract and a hexadecachoron, where the edges of the hexadecachoron are $\frac{5\sqrt2}{4} \approx 1.76777$ times the length of those of the tesseract. Varying the hexadecachoron's edge length to be anything between $\sqrt2 \approx 1.41421$ and $\frac{3\sqrt2}{2} \approx 2.12132$ times that of the tesseract gives a fully symmetric variant of this polychoron.

Variations

In addition to the fully symmetric variations, the disphenoidal enneacontahexachoron has isotopic variants with D₄ symmetry (called the sphenoidal enneacontahexachoron).