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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,6,6,4}*1152c
if this polytope has a name.
Group : SmallGroup(1152,153177)
Rank : 6
Schlafli Type : {2,2,6,6,4}
Number of vertices, edges, etc : 2, 2, 6, 18, 12, 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 : {2,2,3,6,4}*576, {2,2,6,6,2}*576c
   3-fold quotients : {2,2,6,2,4}*384
   4-fold quotients : {2,2,3,6,2}*288
   6-fold quotients : {2,2,3,2,4}*192, {2,2,6,2,2}*192
   9-fold quotients : {2,2,2,2,4}*128
   12-fold quotients : {2,2,3,2,2}*96
   18-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 := ( 6, 7)( 8,11)( 9,13)(10,12)(15,16)(17,20)(18,22)(19,21)(24,25)(26,29)
(27,31)(28,30)(33,34)(35,38)(36,40)(37,39)(42,43)(44,47)(45,49)(46,48)(51,52)
(53,56)(54,58)(55,57)(60,61)(62,65)(63,67)(64,66)(69,70)(71,74)(72,76)
(73,75);;
s3 := ( 5,45)( 6,44)( 7,46)( 8,42)( 9,41)(10,43)(11,48)(12,47)(13,49)(14,54)
(15,53)(16,55)(17,51)(18,50)(19,52)(20,57)(21,56)(22,58)(23,63)(24,62)(25,64)
(26,60)(27,59)(28,61)(29,66)(30,65)(31,67)(32,72)(33,71)(34,73)(35,69)(36,68)
(37,70)(38,75)(39,74)(40,76);;
s4 := ( 8,11)( 9,12)(10,13)(17,20)(18,21)(19,22)(23,32)(24,33)(25,34)(26,38)
(27,39)(28,40)(29,35)(30,36)(31,37)(44,47)(45,48)(46,49)(53,56)(54,57)(55,58)
(59,68)(60,69)(61,70)(62,74)(63,75)(64,76)(65,71)(66,72)(67,73);;
s5 := ( 5,23)( 6,24)( 7,25)( 8,26)( 9,27)(10,28)(11,29)(12,30)(13,31)(14,32)
(15,33)(16,34)(17,35)(18,36)(19,37)(20,38)(21,39)(22,40)(41,59)(42,60)(43,61)
(44,62)(45,63)(46,64)(47,65)(48,66)(49,67)(50,68)(51,69)(52,70)(53,71)(54,72)
(55,73)(56,74)(57,75)(58,76);;
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, 
s3*s4*s5*s4*s3*s4*s5*s4, s4*s5*s4*s5*s4*s5*s4*s5, 
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(76)!(1,2);
s1 := Sym(76)!(3,4);
s2 := Sym(76)!( 6, 7)( 8,11)( 9,13)(10,12)(15,16)(17,20)(18,22)(19,21)(24,25)
(26,29)(27,31)(28,30)(33,34)(35,38)(36,40)(37,39)(42,43)(44,47)(45,49)(46,48)
(51,52)(53,56)(54,58)(55,57)(60,61)(62,65)(63,67)(64,66)(69,70)(71,74)(72,76)
(73,75);
s3 := Sym(76)!( 5,45)( 6,44)( 7,46)( 8,42)( 9,41)(10,43)(11,48)(12,47)(13,49)
(14,54)(15,53)(16,55)(17,51)(18,50)(19,52)(20,57)(21,56)(22,58)(23,63)(24,62)
(25,64)(26,60)(27,59)(28,61)(29,66)(30,65)(31,67)(32,72)(33,71)(34,73)(35,69)
(36,68)(37,70)(38,75)(39,74)(40,76);
s4 := Sym(76)!( 8,11)( 9,12)(10,13)(17,20)(18,21)(19,22)(23,32)(24,33)(25,34)
(26,38)(27,39)(28,40)(29,35)(30,36)(31,37)(44,47)(45,48)(46,49)(53,56)(54,57)
(55,58)(59,68)(60,69)(61,70)(62,74)(63,75)(64,76)(65,71)(66,72)(67,73);
s5 := Sym(76)!( 5,23)( 6,24)( 7,25)( 8,26)( 9,27)(10,28)(11,29)(12,30)(13,31)
(14,32)(15,33)(16,34)(17,35)(18,36)(19,37)(20,38)(21,39)(22,40)(41,59)(42,60)
(43,61)(44,62)(45,63)(46,64)(47,65)(48,66)(49,67)(50,68)(51,69)(52,70)(53,71)
(54,72)(55,73)(56,74)(57,75)(58,76);
poly := sub<Sym(76)|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, s3*s4*s5*s4*s3*s4*s5*s4, 
s4*s5*s4*s5*s4*s5*s4*s5, 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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