Small rhombated hexadecachoron

The small rhombated hexadecachoron is a convex semi-uniform polychoron that is a variant of the rectified icositetrachoron with tesseractic symmetry. As such it can be represented by o4y3o3x, and has 8 cuboctahedra of size y, 16 rhombitetratetrahedra of type x3o3y, and 24 square prisms of type x y4o as cells, with two edge lengths.

Small rhombated hexadecachoron
Rank	4
Type	Semi-uniform
Notation
Coxeter diagram	o4y3o3x
Elements
Cells	24 square prisms, 8 cuboctahedra, 16 rhombitetratetrahedra
Faces	32+64 triangles, 48 squares, 96 rectangles
Edges	96+192
Vertices	96
Vertex figure	Wedge
Measures (edge lengths a (surrounding 2 rhombitetratetrahedra), b (of cuboctahedra))
Circumradius	${\sqrt {\frac {a^{2}+3b^{2}+2ab}{2}}}$
Hypervolume	${\frac {a^{4}+24a^{3}b+54a^{2}b^{2}+84ab^{3}+23b^{4}}{6}}$
Dichoral angles	Co–4–squip: 135°
	Ratet–4–squip: 135°
	Co–3–ratet: 120°
	Ratet–3–ratet: 120°
Central density	1
Related polytopes
Dual	Small notched enneacontihexachoron
Conjugate	Small rhombated hexadecachoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B4, order 384
Convex	Yes
Nature	Tame

Vertex coordinates

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

• $\left(\pm (a+b){\frac {\sqrt {2}}{2}},\,\pm (a+b){\frac {\sqrt {2}}{2}},\,\pm {\frac {b{\sqrt {2}}}{2}},\,0\right)$.