Rank4
TypeSemi-uniform
Notation
Coxeter diagramo4y3o3x
Elements
Cells24 square prisms, 8 cuboctahedra, 16 rhombitetratetrahedra
Faces32+64 triangles, 48 squares, 96 rectangles
Edges96+192
Vertices96
Vertex figureWedge
Measures (edge lengths a (surrounding 2 rhombitetratetrahedra), b (of cuboctahedra))
Circumradius${\displaystyle {\sqrt {\frac {a^{2}+3b^{2}+2ab}{2}}}}$
Hypervolume${\displaystyle {\frac {a^{4}+24a^{3}b+54a^{2}b^{2}+84ab^{3}+23b^{4}}{6}}}$
Dichoral anglesCo–4–squip: 135°
Ratet–4–squip: 135°
Co–3–ratet: 120°
Ratet–3–ratet: 120°
Central density1
Related polytopes
DualSmall notched enneacontihexachoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryB4, order 384
ConvexYes
NatureTame

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.

## Vertex coordinates

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

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