Great rhombated hexadecachoron

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Great rhombated hexadecachoron
Rank4
TypeSemi-uniform
Notation
Coxeter diagramo4z3y3x
Elements
Cells24 square prisms, 8 truncated octahedra, 16 great rhombitetratetrahedra
Faces48 squares, 96 rectangles, 32+64 ditrigons
Edges96+96+192
Vertices192
Vertex figureSphenoid
Measures (edge lengths a, b, c (forming o4c3b3a))
Circumradius
Dichoral anglesToe–4–squip: 135°
 Gratet–4–squip: 135°
 Toe–6–gratet: 120°
 Gratet–6–gratet: 120°
Central density1
Related polytopes
DualSmall sphenoidal hecatonenneacontadichoron
ConjugateGreat rhombated hexadecachoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryB4, order 384
ConvexYes
NatureTame

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[edit | edit source]

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

  • .