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Polytope of Type {3,2,4,4,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,4,4,6}*1152
if this polytope has a name.
Group : SmallGroup(1152,134261)
Rank : 6
Schlafli Type : {3,2,4,4,6}
Number of vertices, edges, etc : 3, 3, 4, 8, 12, 6
Order of s0s1s2s3s4s5 : 12
Order of s0s1s2s3s4s5s4s3s2s1 : 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) :
   2-fold quotients : {3,2,2,4,6}*576a, {3,2,4,2,6}*576
   3-fold quotients : {3,2,4,4,2}*384
   4-fold quotients : {3,2,4,2,3}*288, {3,2,2,2,6}*288
   6-fold quotients : {3,2,2,4,2}*192, {3,2,4,2,2}*192
   8-fold quotients : {3,2,2,2,3}*144
   12-fold quotients : {3,2,2,2,2}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2);;
s2 := ( 4,16)( 5,17)( 6,18)( 7,19)( 8,20)( 9,21)(10,22)(11,23)(12,24)(13,25)
(14,26)(15,27)(28,40)(29,41)(30,42)(31,43)(32,44)(33,45)(34,46)(35,47)(36,48)
(37,49)(38,50)(39,51);;
s3 := (16,22)(17,23)(18,24)(19,25)(20,26)(21,27)(28,31)(29,32)(30,33)(34,37)
(35,38)(36,39)(40,49)(41,50)(42,51)(43,46)(44,47)(45,48);;
s4 := ( 4,28)( 5,30)( 6,29)( 7,31)( 8,33)( 9,32)(10,34)(11,36)(12,35)(13,37)
(14,39)(15,38)(16,40)(17,42)(18,41)(19,43)(20,45)(21,44)(22,46)(23,48)(24,47)
(25,49)(26,51)(27,50);;
s5 := ( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)
(34,35)(37,38)(40,41)(43,44)(46,47)(49,50);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, s3*s4*s5*s4*s3*s4*s5*s4, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(51)!(2,3);
s1 := Sym(51)!(1,2);
s2 := Sym(51)!( 4,16)( 5,17)( 6,18)( 7,19)( 8,20)( 9,21)(10,22)(11,23)(12,24)
(13,25)(14,26)(15,27)(28,40)(29,41)(30,42)(31,43)(32,44)(33,45)(34,46)(35,47)
(36,48)(37,49)(38,50)(39,51);
s3 := Sym(51)!(16,22)(17,23)(18,24)(19,25)(20,26)(21,27)(28,31)(29,32)(30,33)
(34,37)(35,38)(36,39)(40,49)(41,50)(42,51)(43,46)(44,47)(45,48);
s4 := Sym(51)!( 4,28)( 5,30)( 6,29)( 7,31)( 8,33)( 9,32)(10,34)(11,36)(12,35)
(13,37)(14,39)(15,38)(16,40)(17,42)(18,41)(19,43)(20,45)(21,44)(22,46)(23,48)
(24,47)(25,49)(26,51)(27,50);
s5 := Sym(51)!( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)
(31,32)(34,35)(37,38)(40,41)(43,44)(46,47)(49,50);
poly := sub<Sym(51)|s0,s1,s2,s3,s4,s5>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s4*s5*s4*s3*s4*s5*s4, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >; 
 

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