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Polytope of Type {2,2,2,14,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,2,14,6}*1344
if this polytope has a name.
Group : SmallGroup(1344,11709)
Rank : 6
Schlafli Type : {2,2,2,14,6}
Number of vertices, edges, etc : 2, 2, 2, 14, 42, 6
Order of s0s1s2s3s4s5 : 42
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) :
   3-fold quotients : {2,2,2,14,2}*448
   6-fold quotients : {2,2,2,7,2}*224
   7-fold quotients : {2,2,2,2,6}*192
   14-fold quotients : {2,2,2,2,3}*96
   21-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 := (5,6);;
s3 := ( 8,13)( 9,12)(10,11)(15,20)(16,19)(17,18)(22,27)(23,26)(24,25)(29,34)
(30,33)(31,32)(36,41)(37,40)(38,39)(43,48)(44,47)(45,46)(50,55)(51,54)(52,53)
(57,62)(58,61)(59,60)(64,69)(65,68)(66,67)(71,76)(72,75)(73,74)(78,83)(79,82)
(80,81)(85,90)(86,89)(87,88);;
s4 := ( 7,50)( 8,49)( 9,55)(10,54)(11,53)(12,52)(13,51)(14,64)(15,63)(16,69)
(17,68)(18,67)(19,66)(20,65)(21,57)(22,56)(23,62)(24,61)(25,60)(26,59)(27,58)
(28,71)(29,70)(30,76)(31,75)(32,74)(33,73)(34,72)(35,85)(36,84)(37,90)(38,89)
(39,88)(40,87)(41,86)(42,78)(43,77)(44,83)(45,82)(46,81)(47,80)(48,79);;
s5 := ( 7,77)( 8,78)( 9,79)(10,80)(11,81)(12,82)(13,83)(14,70)(15,71)(16,72)
(17,73)(18,74)(19,75)(20,76)(21,84)(22,85)(23,86)(24,87)(25,88)(26,89)(27,90)
(28,56)(29,57)(30,58)(31,59)(32,60)(33,61)(34,62)(35,49)(36,50)(37,51)(38,52)
(39,53)(40,54)(41,55)(42,63)(43,64)(44,65)(45,66)(46,67)(47,68)(48,69);;
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, s2*s3*s2*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*s5*s4*s5, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(90)!(1,2);
s1 := Sym(90)!(3,4);
s2 := Sym(90)!(5,6);
s3 := Sym(90)!( 8,13)( 9,12)(10,11)(15,20)(16,19)(17,18)(22,27)(23,26)(24,25)
(29,34)(30,33)(31,32)(36,41)(37,40)(38,39)(43,48)(44,47)(45,46)(50,55)(51,54)
(52,53)(57,62)(58,61)(59,60)(64,69)(65,68)(66,67)(71,76)(72,75)(73,74)(78,83)
(79,82)(80,81)(85,90)(86,89)(87,88);
s4 := Sym(90)!( 7,50)( 8,49)( 9,55)(10,54)(11,53)(12,52)(13,51)(14,64)(15,63)
(16,69)(17,68)(18,67)(19,66)(20,65)(21,57)(22,56)(23,62)(24,61)(25,60)(26,59)
(27,58)(28,71)(29,70)(30,76)(31,75)(32,74)(33,73)(34,72)(35,85)(36,84)(37,90)
(38,89)(39,88)(40,87)(41,86)(42,78)(43,77)(44,83)(45,82)(46,81)(47,80)(48,79);
s5 := Sym(90)!( 7,77)( 8,78)( 9,79)(10,80)(11,81)(12,82)(13,83)(14,70)(15,71)
(16,72)(17,73)(18,74)(19,75)(20,76)(21,84)(22,85)(23,86)(24,87)(25,88)(26,89)
(27,90)(28,56)(29,57)(30,58)(31,59)(32,60)(33,61)(34,62)(35,49)(36,50)(37,51)
(38,52)(39,53)(40,54)(41,55)(42,63)(43,64)(44,65)(45,66)(46,67)(47,68)(48,69);
poly := sub<Sym(90)|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, 
s2*s3*s2*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*s5*s4*s5, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >; 
 

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