Polytope of Type {3,2,44}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,44}*528
if this polytope has a name.
Group : SmallGroup(528,108)
Rank : 4
Schlafli Type : {3,2,44}
Number of vertices, edges, etc : 3, 3, 44, 44
Order of s₀s₁s₂s₃ : 132
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,44,2} of size 1056
Vertex Figure Of :
   {2,3,2,44} of size 1056
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,22}*264
   4-fold quotients : {3,2,11}*132
   11-fold quotients : {3,2,4}*48
   22-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,88}*1056, {6,2,44}*1056
   3-fold covers : {9,2,44}*1584, {3,6,44}*1584, {3,2,132}*1584
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2);;
s2 := ( 5, 6)( 7, 8)(10,13)(11,12)(14,15)(16,17)(18,21)(19,20)(22,23)(24,25)
(26,29)(27,28)(30,31)(32,33)(34,37)(35,36)(38,39)(40,41)(42,45)(43,44)
(46,47);;
s3 := ( 4,10)( 5, 7)( 6,16)( 8,18)( 9,12)(11,14)(13,24)(15,26)(17,20)(19,22)
(21,32)(23,34)(25,28)(27,30)(29,40)(31,42)(33,36)(35,38)(37,46)(39,43)(41,44)
(45,47);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(47)!(2,3);
s1 := Sym(47)!(1,2);
s2 := Sym(47)!( 5, 6)( 7, 8)(10,13)(11,12)(14,15)(16,17)(18,21)(19,20)(22,23)
(24,25)(26,29)(27,28)(30,31)(32,33)(34,37)(35,36)(38,39)(40,41)(42,45)(43,44)
(46,47);
s3 := Sym(47)!( 4,10)( 5, 7)( 6,16)( 8,18)( 9,12)(11,14)(13,24)(15,26)(17,20)
(19,22)(21,32)(23,34)(25,28)(27,30)(29,40)(31,42)(33,36)(35,38)(37,46)(39,43)
(41,44)(45,47);
poly := sub<Sym(47)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

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