Rectified great hecatonicosachoron
Rectified great hecatonicosachoron  

Rank  4 
Type  Uniform 
Notation  
Bowers style acronym  Righi 
Coxeter diagram  o5x5/2o5o () 
Elements  
Cells  
Faces 

Edges  3600 
Vertices  720 
Vertex figure  Semiuniform pentagonal prism, edge lengths (√5–1)/2 (base) and (1+√5)/2 (side) 
Measures (edge length 1)  
Circumradius  
Hypervolume  
Dichoral angles  Sissid–5/2–did: 144° 
Did–5–did: 144°  
Central density  6 
Number of external pieces  3720 
Level of complexity  14 
Related polytopes  
Army  Rox, edge length 
Regiment  Righi 
Conjugate  Rectified grand stellated hecatonicosachoron 
Convex core  Hecatonicosachoron 
Abstract & topological properties  
Flag count  43200 
Euler characteristic  –960 
Orientable  Yes 
Properties  
Symmetry  H_{4}, order 14400 
Flag orbits  3 
Convex  No 
Nature  Tame 
The rectified great hecatonicosachoron, or righi, is a nonconvex uniform polychoron that consists of 120 small stellated dodecahedra and 120 dodecadodecahedra. Two small stellated dodecahedra and five dodecadodecahedra join at each pentagonal prismatic vertex. As the name suggests, it can be obtained by rectifying the great hecatonicosachoron.
Crosssections[edit  edit source]
Vertex coordinates[edit  edit source]
The vertices of a rectified great hecatonicosachoron of edge length 1 are given by all permutations of:
 ,
 ,
along with even permutations of:
 ,
 ,
 ,
 .
Related polychora[edit  edit source]
The rectified great hecatonicosachoron is the colonel of a regiment with 15 members. Of these, one other besideds the colonel itself is Wythoffian (the rectified grand hecatonicosachoron), two are hemiWythoffian (the pentagrammal antiprismatoverted hexacosihecatonicosachoron and great pentagonal retroprismatoverted dishecatonicosachoron), and one is noble (the medial retropental hecatonicosachoron).
The rectified great hecatonicosachoron also has the same circumradius as the hexagonaldecagonal duoprism.
Uniform polychoron compounds composed of rectified great hecatonicosachora include:
 Rectified great diacositetracontachoron (2)
 Rectified great chirohexacosichoron (5)
 Rectified great dishexacosichoron (10)
External links[edit  edit source]
 Bowers, Jonathan. "Category 5: Pentagonal Rectates" (#88).
 Klitzing, Richard. "righi".