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Polytope of Type {2,2,3,6,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,3,6,8}*1152
if this polytope has a name.
Group : SmallGroup(1152,152550)
Rank : 6
Schlafli Type : {2,2,3,6,8}
Number of vertices, edges, etc : 2, 2, 3, 9, 24, 8
Order of s0s1s2s3s4s5 : 24
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
   3-fold quotients : {2,2,3,2,8}*384
   4-fold quotients : {2,2,3,6,2}*288
   6-fold quotients : {2,2,3,2,4}*192
   12-fold quotients : {2,2,3,2,2}*96
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, 9)( 6, 8)( 7,10)(11,12)(14,18)(15,17)(16,19)(20,21)(23,27)(24,26)
(25,28)(29,30)(32,36)(33,35)(34,37)(38,39)(41,45)(42,44)(43,46)(47,48)(50,54)
(51,53)(52,55)(56,57)(59,63)(60,62)(61,64)(65,66)(68,72)(69,71)(70,73)
(74,75);;
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)(41,59)(42,60)(43,61)(44,65)(45,66)(46,67)
(47,62)(48,63)(49,64)(50,68)(51,69)(52,70)(53,74)(54,75)(55,76)(56,71)(57,72)
(58,73);;
s5 := ( 5,41)( 6,42)( 7,43)( 8,44)( 9,45)(10,46)(11,47)(12,48)(13,49)(14,50)
(15,51)(16,52)(17,53)(18,54)(19,55)(20,56)(21,57)(22,58)(23,68)(24,69)(25,70)
(26,71)(27,72)(28,73)(29,74)(30,75)(31,76)(32,59)(33,60)(34,61)(35,62)(36,63)
(37,64)(38,65)(39,66)(40,67);;
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, 
s2*s3*s2*s3*s2*s3, s3*s4*s5*s4*s3*s4*s5*s4, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
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, 9)( 6, 8)( 7,10)(11,12)(14,18)(15,17)(16,19)(20,21)(23,27)
(24,26)(25,28)(29,30)(32,36)(33,35)(34,37)(38,39)(41,45)(42,44)(43,46)(47,48)
(50,54)(51,53)(52,55)(56,57)(59,63)(60,62)(61,64)(65,66)(68,72)(69,71)(70,73)
(74,75);
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)(41,59)(42,60)(43,61)(44,65)(45,66)
(46,67)(47,62)(48,63)(49,64)(50,68)(51,69)(52,70)(53,74)(54,75)(55,76)(56,71)
(57,72)(58,73);
s5 := Sym(76)!( 5,41)( 6,42)( 7,43)( 8,44)( 9,45)(10,46)(11,47)(12,48)(13,49)
(14,50)(15,51)(16,52)(17,53)(18,54)(19,55)(20,56)(21,57)(22,58)(23,68)(24,69)
(25,70)(26,71)(27,72)(28,73)(29,74)(30,75)(31,76)(32,59)(33,60)(34,61)(35,62)
(36,63)(37,64)(38,65)(39,66)(40,67);
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, s2*s3*s2*s3*s2*s3, s3*s4*s5*s4*s3*s4*s5*s4, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >; 
 

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