Faceted rectified icositetrachoron
(Redirected from Frico)
Faceted rectified icositetrachoron  

Rank  4 
Type  Uniform 
Notation  
Bowers style acronym  Frico 
Coxeter diagram  x3x4o3/2o4*a (/2) 
Elements  
Cells 

Faces  144 squares, 96 hexagons 
Edges  288 
Vertices  96 
Vertex figure  Triangular retroprism, edge lengths √2 (base) and √3 (sides) 
Edge figure  cube 4 toe 6 toe 6 toe 4 
Measures (edge length 1)  
Circumradius  
Hypervolume  39 
Dichoral angle  Toe–6–toe: 60° Cube–4–toe: 45° 
Central density  5 
Number of external pieces  1032 
Level of complexity  23 
Related polytopes  
Army  Rico 
Regiment  Rico 
Conjugate  None 
Convex core  Icositetrachoron 
Abstract & topological properties  
Flag count  4608 
Euler characteristic  0 
Orientable  Yes 
Properties  
Symmetry  F_{4}, order 1152 
Flag orbits  4 
Convex  No 
Nature  Tame 
The faceted rectified icositetrachoron, or frico, is a nonconvex uniform polychoron that consists of 24 cubes and 24 truncated octahedra. Two cubes and six truncated octahedra join at each vertex.
Gallery[edit  edit source]
Vertex coordinates[edit  edit source]
Its vertices are the same as those of its regiment colonel, the rectified icositetrachoron.
External links[edit  edit source]
 Bowers, Jonathan. "Category 3: Triangular Rectates" (#46).
 Bowers, Jonathan. "Category 6: Sphenoverts" (#46  recount under tesseractic symmetry).
 Klitzing, Richard. "frico".