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Polytope of Type {44,6}

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