Questions?
See the FAQ
or other info.

Polytope of Type {20,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,6}*480a
if this polytope has a name.
Group : SmallGroup(480,956)
Rank : 3
Schlafli Type : {20,6}
Number of vertices, edges, etc : 40, 120, 12
Order of s0s1s2 : 20
Order of s0s1s2s1 : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {20,6,2} of size 960
Vertex Figure Of :
   {2,20,6} of size 960
   {4,20,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,6}*240e
   4-fold quotients : {5,6}*120b, {10,3}*120a
   8-fold quotients : {5,3}*60
Covers (Minimal Covers in Boldface) :
   2-fold covers : {40,6}*960a, {40,6}*960b, {20,6}*960c
   3-fold covers : {60,6}*1440a
   4-fold covers : {80,6}*1920a, {80,6}*1920b, {20,12}*1920g, {40,6}*1920f, {20,6}*1920d, {20,12}*1920l, {40,6}*1920h
Permutation Representation (GAP) :
s0 := (2,3)(6,7)(8,9);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := (6,9)(7,8);;
poly := Group([s0,s1,s2]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0, 
s0*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(9)!(2,3)(6,7)(8,9);
s1 := Sym(9)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(9)!(6,9)(7,8);
poly := sub<Sym(9)|s0,s1,s2>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0, 
s0*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1 >; 
 
References : None.
to this polytope