Great rhombated hexadecachoron

Great rhombated hexadecachoron
Rank	4
Type	Semi-uniform
Space	Spherical
Notation
Coxeter diagram	o4z3y3x
Elements
Cells	24 square prisms, 8 truncated octahedra, 16 great rhombitetratetrahedra
Faces	48 squares, 96 rectangles, 32+64 ditrigons
Edges	96+96+192
Vertices	192
Vertex figure	Sphenoid
Measures (edge lengths a, b, c (forming o4c3b3a))
Circumradius	$\sqrt{\frac{a^2+2b^2+3c^2+2ab+2ac+4bc}{2}}$
Dichoral angles	Toe–4–squip: 135°
	Gratet–4–squip: 135°
	Toe–6–gratet: 120°
	Gratet–6–gratet: 120°
Central density	1
Related polytopes
Dual	Small sphenoidal hecatonenneacontadichoron
Conjugate	Great rhombated hexadecachoron
Abstract properties
Euler characteristic	0
Topological properties
Orientable	Yes
Properties
Symmetry	B4, order 384
Convex	Yes
Nature	Tame

The great rhombated hexadecachoron is a convex semi-uniform polychoron that is a variant of the truncated icositetrachoron with tesseractic symmetry. As such it can be represented by o4z3y3x, and has 8 truncated octahedra of form o4z3y, 16 great rhombitetratetrahedra of type x3y3z, and 24 square prisms of type x z4o as cells, with 3 edge lengths.

Vertex coordinates

A great rhombated hexadecachoron with edge lengths a and b has vertices given by all permutations of:

• $\left(±(a+b+c)\frac{\sqrt2}{2},\,±(b+c)\frac{\sqrt2}{2},\,±c\frac{\sqrt2}{2},\,0\right).$