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

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

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