# Retroinverted hexacosihecatonicosachoron

Retroinverted hexacosihecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymRixhi
Elements
Cells
Faces
Edges3600
Vertices720
Vertex figurePentagonal toroprism, edge lengths 1 (squares), (5+5)/2 (sides of triangles)
Edge figureoct.oct.tid.tid.tid
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {5+2{\sqrt {5}}}}\approx 3.07768}$
Hypervolume${\displaystyle 75{\frac {61+27{\sqrt {5}}}{4}}\approx 2275.75941}$
Dichoral angleOct–3–oct: ${\displaystyle \arccos \left(-{\frac {1+3{\sqrt {5}}}{8}}\right)\approx 164.47751^{\circ }}$
Tid–3–oct: ${\displaystyle \arccos \left(-{\frac {\sqrt {7-3{\sqrt {5}}}}{4}}\right)\approx 97.76124^{\circ }}$
Tid–10–tid: 36°
Number of external pieces17400
Level of complexity38
Related polytopes
ArmyRox
RegimentRox
ConjugateFaceted rectified great faceted hexacosichoron
Convex coreHecatonicosachoron
Abstract & topological properties
Flag count72000
Euler characteristic720
OrientableYes
Properties
SymmetryH4, order 14400
Flag orbits5
ConvexNo
NatureTame

The retroinverted hexacosihecatonicosachoron, or rixhi, is a nonconvex uniform polychoron that consists of 120 truncated dodecahedra and 600 octahedra. 5 octahedra and 10 truncated dodecahedra join at each vertex.

It is in the regiment of the rectified hexacosichoron.

## Vertex coordinates

Its vertices are the same as those of its regiment colonel, the rectified hexacosichoron.