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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,6,3}*576
if this polytope has a name.
Group : SmallGroup(576,8589)
Rank : 6
Schlafli Type : {2,2,4,6,3}
Number of vertices, edges, etc : 2, 2, 4, 12, 9, 3
Order of s0s1s2s3s4s5 : 12
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,4,6,3,2} of size 1152
Vertex Figure Of :
   {2,2,2,4,6,3} of size 1152
   {3,2,2,4,6,3} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,2,6,3}*288
   3-fold quotients : {2,2,4,2,3}*192
   6-fold quotients : {2,2,2,2,3}*96
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,4,4,6,3}*1152, {4,2,4,6,3}*1152, {2,2,8,6,3}*1152, {2,2,4,6,6}*1152c
   3-fold covers : {2,2,4,6,9}*1728, {2,2,4,6,3}*1728a, {2,2,12,6,3}*1728b, {2,6,4,6,3}*1728, {6,2,4,6,3}*1728
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 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);;
s3 := ( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(23,32)(24,34)(25,33)(26,35)
(27,37)(28,36)(29,38)(30,40)(31,39)(42,43)(45,46)(48,49)(51,52)(54,55)(57,58)
(59,68)(60,70)(61,69)(62,71)(63,73)(64,72)(65,74)(66,76)(67,75);;
s4 := ( 5,42)( 6,41)( 7,43)( 8,48)( 9,47)(10,49)(11,45)(12,44)(13,46)(14,51)
(15,50)(16,52)(17,57)(18,56)(19,58)(20,54)(21,53)(22,55)(23,60)(24,59)(25,61)
(26,66)(27,65)(28,67)(29,63)(30,62)(31,64)(32,69)(33,68)(34,70)(35,75)(36,74)
(37,76)(38,72)(39,71)(40,73);;
s5 := ( 5,44)( 6,46)( 7,45)( 8,41)( 9,43)(10,42)(11,47)(12,49)(13,48)(14,53)
(15,55)(16,54)(17,50)(18,52)(19,51)(20,56)(21,58)(22,57)(23,62)(24,64)(25,63)
(26,59)(27,61)(28,60)(29,65)(30,67)(31,66)(32,71)(33,73)(34,72)(35,68)(36,70)
(37,69)(38,74)(39,76)(40,75);;
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, 
s4*s5*s4*s5*s4*s5, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s5*s3*s4*s3*s4*s5*s3*s4*s3*s4 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(76)!(1,2);
s1 := Sym(76)!(3,4);
s2 := 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);
s3 := Sym(76)!( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(23,32)(24,34)(25,33)
(26,35)(27,37)(28,36)(29,38)(30,40)(31,39)(42,43)(45,46)(48,49)(51,52)(54,55)
(57,58)(59,68)(60,70)(61,69)(62,71)(63,73)(64,72)(65,74)(66,76)(67,75);
s4 := Sym(76)!( 5,42)( 6,41)( 7,43)( 8,48)( 9,47)(10,49)(11,45)(12,44)(13,46)
(14,51)(15,50)(16,52)(17,57)(18,56)(19,58)(20,54)(21,53)(22,55)(23,60)(24,59)
(25,61)(26,66)(27,65)(28,67)(29,63)(30,62)(31,64)(32,69)(33,68)(34,70)(35,75)
(36,74)(37,76)(38,72)(39,71)(40,73);
s5 := Sym(76)!( 5,44)( 6,46)( 7,45)( 8,41)( 9,43)(10,42)(11,47)(12,49)(13,48)
(14,53)(15,55)(16,54)(17,50)(18,52)(19,51)(20,56)(21,58)(22,57)(23,62)(24,64)
(25,63)(26,59)(27,61)(28,60)(29,65)(30,67)(31,66)(32,71)(33,73)(34,72)(35,68)
(36,70)(37,69)(38,74)(39,76)(40,75);
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, s4*s5*s4*s5*s4*s5, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s5*s3*s4*s3*s4*s5*s3*s4*s3*s4 >; 
 

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