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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,6,6}*576e
if this polytope has a name.
Group : SmallGroup(576,8659)
Rank : 5
Schlafli Type : {2,4,6,6}
Number of vertices, edges, etc : 2, 4, 12, 18, 6
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,4,6,6,2} of size 1152
   {2,4,6,6,3} of size 1728
Vertex Figure Of :
   {2,2,4,6,6} of size 1152
   {3,2,4,6,6} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,4,3,6}*288
   3-fold quotients : {2,4,6,2}*192c
   6-fold quotients : {2,4,3,2}*96
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,4,12,6}*1152e, {2,4,12,6}*1152g, {2,4,6,12}*1152e, {2,4,6,6}*1152b
   3-fold covers : {2,4,18,6}*1728d, {2,4,6,6}*1728d, {2,4,6,6}*1728i
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)
(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)
(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,60)(61,62)(63,64)(65,66)
(67,68)(69,70)(71,72)(73,74);;
s2 := ( 4, 5)( 7,11)( 8,13)( 9,12)(10,14)(15,27)(16,29)(17,28)(18,30)(19,35)
(20,37)(21,36)(22,38)(23,31)(24,33)(25,32)(26,34)(40,41)(43,47)(44,49)(45,48)
(46,50)(51,63)(52,65)(53,64)(54,66)(55,71)(56,73)(57,72)(58,74)(59,67)(60,69)
(61,68)(62,70);;
s3 := ( 3,55)( 4,56)( 5,58)( 6,57)( 7,51)( 8,52)( 9,54)(10,53)(11,59)(12,60)
(13,62)(14,61)(15,43)(16,44)(17,46)(18,45)(19,39)(20,40)(21,42)(22,41)(23,47)
(24,48)(25,50)(26,49)(27,67)(28,68)(29,70)(30,69)(31,63)(32,64)(33,66)(34,65)
(35,71)(36,72)(37,74)(38,73);;
s4 := ( 7,11)( 8,12)( 9,13)(10,14)(19,23)(20,24)(21,25)(22,26)(31,35)(32,36)
(33,37)(34,38)(43,47)(44,48)(45,49)(46,50)(55,59)(56,60)(57,61)(58,62)(67,71)
(68,72)(69,73)(70,74);;
poly := Group([s0,s1,s2,s3,s4]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s1*s2, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(74)!(1,2);
s1 := Sym(74)!( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)
(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)
(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,60)(61,62)(63,64)
(65,66)(67,68)(69,70)(71,72)(73,74);
s2 := Sym(74)!( 4, 5)( 7,11)( 8,13)( 9,12)(10,14)(15,27)(16,29)(17,28)(18,30)
(19,35)(20,37)(21,36)(22,38)(23,31)(24,33)(25,32)(26,34)(40,41)(43,47)(44,49)
(45,48)(46,50)(51,63)(52,65)(53,64)(54,66)(55,71)(56,73)(57,72)(58,74)(59,67)
(60,69)(61,68)(62,70);
s3 := Sym(74)!( 3,55)( 4,56)( 5,58)( 6,57)( 7,51)( 8,52)( 9,54)(10,53)(11,59)
(12,60)(13,62)(14,61)(15,43)(16,44)(17,46)(18,45)(19,39)(20,40)(21,42)(22,41)
(23,47)(24,48)(25,50)(26,49)(27,67)(28,68)(29,70)(30,69)(31,63)(32,64)(33,66)
(34,65)(35,71)(36,72)(37,74)(38,73);
s4 := Sym(74)!( 7,11)( 8,12)( 9,13)(10,14)(19,23)(20,24)(21,25)(22,26)(31,35)
(32,36)(33,37)(34,38)(43,47)(44,48)(45,49)(46,50)(55,59)(56,60)(57,61)(58,62)
(67,71)(68,72)(69,73)(70,74);
poly := sub<Sym(74)|s0,s1,s2,s3,s4>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s1*s2, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3 >; 
 

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