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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,4,6}*768
if this polytope has a name.
Group : SmallGroup(768,1076197)
Rank : 6
Schlafli Type : {2,2,4,4,6}
Number of vertices, edges, etc : 2, 2, 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 : {2,2,2,4,6}*384a, {2,2,4,2,6}*384
   3-fold quotients : {2,2,4,4,2}*256
   4-fold quotients : {2,2,4,2,3}*192, {2,2,2,2,6}*192
   6-fold quotients : {2,2,2,4,2}*128, {2,2,4,2,2}*128
   8-fold quotients : {2,2,2,2,3}*96
   12-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 5,17)( 6,18)( 7,19)( 8,20)( 9,21)(10,22)(11,23)(12,24)(13,25)(14,26)
(15,27)(16,28)(29,41)(30,42)(31,43)(32,44)(33,45)(34,46)(35,47)(36,48)(37,49)
(38,50)(39,51)(40,52);;
s3 := (17,23)(18,24)(19,25)(20,26)(21,27)(22,28)(29,32)(30,33)(31,34)(35,38)
(36,39)(37,40)(41,50)(42,51)(43,52)(44,47)(45,48)(46,49);;
s4 := ( 5,29)( 6,31)( 7,30)( 8,32)( 9,34)(10,33)(11,35)(12,37)(13,36)(14,38)
(15,40)(16,39)(17,41)(18,43)(19,42)(20,44)(21,46)(22,45)(23,47)(24,49)(25,48)
(26,50)(27,52)(28,51);;
s5 := ( 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);;
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*s1*s0*s1, 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, 
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(52)!(1,2);
s1 := Sym(52)!(3,4);
s2 := Sym(52)!( 5,17)( 6,18)( 7,19)( 8,20)( 9,21)(10,22)(11,23)(12,24)(13,25)
(14,26)(15,27)(16,28)(29,41)(30,42)(31,43)(32,44)(33,45)(34,46)(35,47)(36,48)
(37,49)(38,50)(39,51)(40,52);
s3 := Sym(52)!(17,23)(18,24)(19,25)(20,26)(21,27)(22,28)(29,32)(30,33)(31,34)
(35,38)(36,39)(37,40)(41,50)(42,51)(43,52)(44,47)(45,48)(46,49);
s4 := Sym(52)!( 5,29)( 6,31)( 7,30)( 8,32)( 9,34)(10,33)(11,35)(12,37)(13,36)
(14,38)(15,40)(16,39)(17,41)(18,43)(19,42)(20,44)(21,46)(22,45)(23,47)(24,49)
(25,48)(26,50)(27,52)(28,51);
s5 := Sym(52)!( 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);
poly := sub<Sym(52)|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*s1*s0*s1, 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, 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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