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Polytope of Type {6,44}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,44}*528b
if this polytope has a name.
Group : SmallGroup(528,160)
Rank : 3
Schlafli Type : {6,44}
Number of vertices, edges, etc : 6, 132, 44
Order of s0s1s2 : 33
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,44,2} of size 1056
Vertex Figure Of :
   {2,6,44} of size 1056
Quotients (Maximal Quotients in Boldface) :
   11-fold quotients : {6,4}*48b
   22-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,44}*1056
   3-fold covers : {18,44}*1584b, {6,132}*1584d
Permutation Representation (GAP) :
s0 := ( 2, 3)( 6, 7)(10,11)(14,15)(18,19)(22,23)(26,27)(30,31)(34,35)(38,39)
(42,43);;
s1 := ( 3, 4)( 5,41)( 6,42)( 7,44)( 8,43)( 9,37)(10,38)(11,40)(12,39)(13,33)
(14,34)(15,36)(16,35)(17,29)(18,30)(19,32)(20,31)(21,25)(22,26)(23,28)
(24,27);;
s2 := ( 1, 8)( 2, 7)( 3, 6)( 4, 5)( 9,44)(10,43)(11,42)(12,41)(13,40)(14,39)
(15,38)(16,37)(17,36)(18,35)(19,34)(20,33)(21,32)(22,31)(23,30)(24,29)(25,28)
(26,27);;
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*s0*s1, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(44)!( 2, 3)( 6, 7)(10,11)(14,15)(18,19)(22,23)(26,27)(30,31)(34,35)
(38,39)(42,43);
s1 := Sym(44)!( 3, 4)( 5,41)( 6,42)( 7,44)( 8,43)( 9,37)(10,38)(11,40)(12,39)
(13,33)(14,34)(15,36)(16,35)(17,29)(18,30)(19,32)(20,31)(21,25)(22,26)(23,28)
(24,27);
s2 := Sym(44)!( 1, 8)( 2, 7)( 3, 6)( 4, 5)( 9,44)(10,43)(11,42)(12,41)(13,40)
(14,39)(15,38)(16,37)(17,36)(18,35)(19,34)(20,33)(21,32)(22,31)(23,30)(24,29)
(25,28)(26,27);
poly := sub<Sym(44)|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*s0*s1, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 
References : None.
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