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Polytope of Type {68,2,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {68,2,6}*1632
if this polytope has a name.
Group : SmallGroup(1632,1088)
Rank : 4
Schlafli Type : {68,2,6}
Number of vertices, edges, etc : 68, 68, 6, 6
Order of s0s1s2s3 : 204
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) :
   2-fold quotients : {68,2,3}*816, {34,2,6}*816
   3-fold quotients : {68,2,2}*544
   4-fold quotients : {17,2,6}*408, {34,2,3}*408
   6-fold quotients : {34,2,2}*272
   8-fold quotients : {17,2,3}*204
   12-fold quotients : {17,2,2}*136
   17-fold quotients : {4,2,6}*96
   34-fold quotients : {4,2,3}*48, {2,2,6}*48
   51-fold quotients : {4,2,2}*32
   68-fold quotients : {2,2,3}*24
   102-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2,17)( 3,16)( 4,15)( 5,14)( 6,13)( 7,12)( 8,11)( 9,10)(19,34)(20,33)
(21,32)(22,31)(23,30)(24,29)(25,28)(26,27)(35,52)(36,68)(37,67)(38,66)(39,65)
(40,64)(41,63)(42,62)(43,61)(44,60)(45,59)(46,58)(47,57)(48,56)(49,55)(50,54)
(51,53);;
s1 := ( 1,36)( 2,35)( 3,51)( 4,50)( 5,49)( 6,48)( 7,47)( 8,46)( 9,45)(10,44)
(11,43)(12,42)(13,41)(14,40)(15,39)(16,38)(17,37)(18,53)(19,52)(20,68)(21,67)
(22,66)(23,65)(24,64)(25,63)(26,62)(27,61)(28,60)(29,59)(30,58)(31,57)(32,56)
(33,55)(34,54);;
s2 := (71,72)(73,74);;
s3 := (69,73)(70,71)(72,74);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(74)!( 2,17)( 3,16)( 4,15)( 5,14)( 6,13)( 7,12)( 8,11)( 9,10)(19,34)
(20,33)(21,32)(22,31)(23,30)(24,29)(25,28)(26,27)(35,52)(36,68)(37,67)(38,66)
(39,65)(40,64)(41,63)(42,62)(43,61)(44,60)(45,59)(46,58)(47,57)(48,56)(49,55)
(50,54)(51,53);
s1 := Sym(74)!( 1,36)( 2,35)( 3,51)( 4,50)( 5,49)( 6,48)( 7,47)( 8,46)( 9,45)
(10,44)(11,43)(12,42)(13,41)(14,40)(15,39)(16,38)(17,37)(18,53)(19,52)(20,68)
(21,67)(22,66)(23,65)(24,64)(25,63)(26,62)(27,61)(28,60)(29,59)(30,58)(31,57)
(32,56)(33,55)(34,54);
s2 := Sym(74)!(71,72)(73,74);
s3 := Sym(74)!(69,73)(70,71)(72,74);
poly := sub<Sym(74)|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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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