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Polytope of Type {2,3,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,6}*1152
if this polytope has a name.
Group : SmallGroup(1152,155485)
Rank : 4
Schlafli Type : {2,3,6}
Number of vertices, edges, etc : 2, 48, 144, 96
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,3,6}*384
   4-fold quotients : {2,3,6}*288
   12-fold quotients : {2,3,6}*96
   16-fold quotients : {2,3,6}*72
   24-fold quotients : {2,3,3}*48
   48-fold quotients : {2,3,2}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 5, 6)( 7,14)( 8,13)( 9,11)(10,12)(15,16)(19,35)(20,36)(21,38)(22,37)
(23,46)(24,45)(25,43)(26,44)(27,41)(28,42)(29,40)(30,39)(31,48)(32,47)(33,49)
(34,50);;
s2 := ( 3,19)( 4,21)( 5,20)( 6,22)( 7,26)( 8,24)( 9,25)(10,23)(11,34)(12,32)
(13,33)(14,31)(15,30)(16,28)(17,29)(18,27)(36,37)(39,42)(43,50)(44,48)(45,49)
(46,47);;
s3 := ( 3,17)( 4,18)( 5,16)( 6,15)( 7, 8)(13,14)(19,33)(20,34)(21,32)(22,31)
(23,24)(29,30)(35,49)(36,50)(37,48)(38,47)(39,40)(45,46);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(50)!(1,2);
s1 := Sym(50)!( 5, 6)( 7,14)( 8,13)( 9,11)(10,12)(15,16)(19,35)(20,36)(21,38)
(22,37)(23,46)(24,45)(25,43)(26,44)(27,41)(28,42)(29,40)(30,39)(31,48)(32,47)
(33,49)(34,50);
s2 := Sym(50)!( 3,19)( 4,21)( 5,20)( 6,22)( 7,26)( 8,24)( 9,25)(10,23)(11,34)
(12,32)(13,33)(14,31)(15,30)(16,28)(17,29)(18,27)(36,37)(39,42)(43,50)(44,48)
(45,49)(46,47);
s3 := Sym(50)!( 3,17)( 4,18)( 5,16)( 6,15)( 7, 8)(13,14)(19,33)(20,34)(21,32)
(22,31)(23,24)(29,30)(35,49)(36,50)(37,48)(38,47)(39,40)(45,46);
poly := sub<Sym(50)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2 >; 
 

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