Retroinverted hexacosihecatonicosachoron
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.
Retroinverted hexacosihecatonicosachoron  

Rank  4 
Type  Uniform 
Notation  
Bowers style acronym  Rixhi 
Elements  
Cells 

Faces  
Edges  3600 
Vertices  720 
Vertex figure  Pentagonal toroprism, edge lengths 1 (squares), √(5+√5)/2 (sides of triangles) 
Edge figure  oct.oct.tid.tid.tid 
Measures (edge length 1)  
Circumradius  
Hypervolume  
Dichoral angle  Oct–3–oct: Tid–3–oct: Tid–10–tid: 36° 
Number of external pieces  17400 
Level of complexity  38 
Related polytopes  
Army  Rox 
Regiment  Rox 
Conjugate  Faceted rectified great faceted hexacosichoron 
Convex core  Hecatonicosachoron 
Abstract & topological properties  
Flag count  72000 
Euler characteristic  720 
Orientable  Yes 
Properties  
Symmetry  H_{4}, order 14400 
Flag orbits  5 
Convex  No 
Nature  Tame 
It is in the regiment of the rectified hexacosichoron.
Gallery edit
Vertex coordinates edit
Its vertices are the same as those of its regiment colonel, the rectified hexacosichoron.
External links edit
 Bowers, Jonathan. "Category 5: Pentagonal Rectates" (#78).
 Klitzing, Richard. "rixhi".