Retroinverted hexacosihecatonicosachoron
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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 
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.
Gallery[edit  edit source]
Vertex coordinates[edit  edit source]
Its vertices are the same as those of its regiment colonel, the rectified hexacosichoron.
External links[edit  edit source]
 Bowers, Jonathan. "Category 5: Pentagonal Rectates" (#78).
 Klitzing, Richard. "rixhi".