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Polytope of Type {4,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12}*480b
if this polytope has a name.
Group : SmallGroup(480,951)
Rank : 3
Schlafli Type : {4,12}
Number of vertices, edges, etc : 20, 120, 60
Order of s0s1s2 : 10
Order of s0s1s2s1 : 3
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {4,12,2} of size 960
Vertex Figure Of :
   {2,4,12} of size 960
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,6}*240b
   4-fold quotients : {4,6}*120
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,24}*960a, {4,24}*960b, {4,12}*960b
   3-fold covers : {12,12}*1440b
   4-fold covers : {4,12}*1920a, {8,12}*1920a, {8,12}*1920b, {4,24}*1920c, {4,24}*1920d
Permutation Representation (GAP) :
s0 := (3,4)(7,9);;
s1 := (1,3)(2,4)(6,7)(8,9);;
s2 := (1,2)(5,6);;
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, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(9)!(3,4)(7,9);
s1 := Sym(9)!(1,3)(2,4)(6,7)(8,9);
s2 := Sym(9)!(1,2)(5,6);
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, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1 >; 
 
References : None.
to this polytope