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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,6,4,4}*1152
if this polytope has a name.
Group : SmallGroup(1152,134261)
Rank : 6
Schlafli Type : {3,2,6,4,4}
Number of vertices, edges, etc : 3, 3, 6, 12, 8, 4
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 : {3,2,6,2,4}*576, {3,2,6,4,2}*576a
   3-fold quotients : {3,2,2,4,4}*384
   4-fold quotients : {3,2,3,2,4}*288, {3,2,6,2,2}*288
   6-fold quotients : {3,2,2,2,4}*192, {3,2,2,4,2}*192
   8-fold quotients : {3,2,3,2,2}*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 := ( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)(32,33)
(35,36)(38,39)(41,42)(44,45)(47,48)(50,51);;
s3 := ( 4,17)( 5,16)( 6,18)( 7,20)( 8,19)( 9,21)(10,23)(11,22)(12,24)(13,26)
(14,25)(15,27)(28,41)(29,40)(30,42)(31,44)(32,43)(33,45)(34,47)(35,46)(36,48)
(37,50)(38,49)(39,51);;
s4 := (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);;
s5 := ( 4,28)( 5,29)( 6,30)( 7,31)( 8,32)( 9,33)(10,34)(11,35)(12,36)(13,37)
(14,38)(15,39)(16,40)(17,41)(18,42)(19,43)(20,44)(21,45)(22,46)(23,47)(24,48)
(25,49)(26,50)(27,51);;
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*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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(51)!(2,3);
s1 := Sym(51)!(1,2);
s2 := Sym(51)!( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)
(32,33)(35,36)(38,39)(41,42)(44,45)(47,48)(50,51);
s3 := Sym(51)!( 4,17)( 5,16)( 6,18)( 7,20)( 8,19)( 9,21)(10,23)(11,22)(12,24)
(13,26)(14,25)(15,27)(28,41)(29,40)(30,42)(31,44)(32,43)(33,45)(34,47)(35,46)
(36,48)(37,50)(38,49)(39,51);
s4 := 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);
s5 := Sym(51)!( 4,28)( 5,29)( 6,30)( 7,31)( 8,32)( 9,33)(10,34)(11,35)(12,36)
(13,37)(14,38)(15,39)(16,40)(17,41)(18,42)(19,43)(20,44)(21,45)(22,46)(23,47)
(24,48)(25,49)(26,50)(27,51);
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*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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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