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Polytope of Type {28,6,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {28,6,2,2}*1344a
if this polytope has a name.
Group : SmallGroup(1344,11517)
Rank : 5
Schlafli Type : {28,6,2,2}
Number of vertices, edges, etc : 28, 84, 6, 2, 2
Order of s0s1s2s3s4 : 84
Order of s0s1s2s3s4s3s2s1 : 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 : {14,6,2,2}*672
   3-fold quotients : {28,2,2,2}*448
   6-fold quotients : {14,2,2,2}*224
   7-fold quotients : {4,6,2,2}*192a
   12-fold quotients : {7,2,2,2}*112
   14-fold quotients : {2,6,2,2}*96
   21-fold quotients : {4,2,2,2}*64
   28-fold quotients : {2,3,2,2}*48
   42-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 7)( 3, 6)( 4, 5)( 9,14)(10,13)(11,12)(16,21)(17,20)(18,19)(23,28)
(24,27)(25,26)(30,35)(31,34)(32,33)(37,42)(38,41)(39,40)(43,64)(44,70)(45,69)
(46,68)(47,67)(48,66)(49,65)(50,71)(51,77)(52,76)(53,75)(54,74)(55,73)(56,72)
(57,78)(58,84)(59,83)(60,82)(61,81)(62,80)(63,79);;
s1 := ( 1,44)( 2,43)( 3,49)( 4,48)( 5,47)( 6,46)( 7,45)( 8,58)( 9,57)(10,63)
(11,62)(12,61)(13,60)(14,59)(15,51)(16,50)(17,56)(18,55)(19,54)(20,53)(21,52)
(22,65)(23,64)(24,70)(25,69)(26,68)(27,67)(28,66)(29,79)(30,78)(31,84)(32,83)
(33,82)(34,81)(35,80)(36,72)(37,71)(38,77)(39,76)(40,75)(41,74)(42,73);;
s2 := ( 1, 8)( 2, 9)( 3,10)( 4,11)( 5,12)( 6,13)( 7,14)(22,29)(23,30)(24,31)
(25,32)(26,33)(27,34)(28,35)(43,50)(44,51)(45,52)(46,53)(47,54)(48,55)(49,56)
(64,71)(65,72)(66,73)(67,74)(68,75)(69,76)(70,77);;
s3 := (85,86);;
s4 := (87,88);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(88)!( 2, 7)( 3, 6)( 4, 5)( 9,14)(10,13)(11,12)(16,21)(17,20)(18,19)
(23,28)(24,27)(25,26)(30,35)(31,34)(32,33)(37,42)(38,41)(39,40)(43,64)(44,70)
(45,69)(46,68)(47,67)(48,66)(49,65)(50,71)(51,77)(52,76)(53,75)(54,74)(55,73)
(56,72)(57,78)(58,84)(59,83)(60,82)(61,81)(62,80)(63,79);
s1 := Sym(88)!( 1,44)( 2,43)( 3,49)( 4,48)( 5,47)( 6,46)( 7,45)( 8,58)( 9,57)
(10,63)(11,62)(12,61)(13,60)(14,59)(15,51)(16,50)(17,56)(18,55)(19,54)(20,53)
(21,52)(22,65)(23,64)(24,70)(25,69)(26,68)(27,67)(28,66)(29,79)(30,78)(31,84)
(32,83)(33,82)(34,81)(35,80)(36,72)(37,71)(38,77)(39,76)(40,75)(41,74)(42,73);
s2 := Sym(88)!( 1, 8)( 2, 9)( 3,10)( 4,11)( 5,12)( 6,13)( 7,14)(22,29)(23,30)
(24,31)(25,32)(26,33)(27,34)(28,35)(43,50)(44,51)(45,52)(46,53)(47,54)(48,55)
(49,56)(64,71)(65,72)(66,73)(67,74)(68,75)(69,76)(70,77);
s3 := Sym(88)!(85,86);
s4 := Sym(88)!(87,88);
poly := sub<Sym(88)|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*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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