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Polytope of Type {2,42,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,42,6}*1008a
if this polytope has a name.
Group : SmallGroup(1008,922)
Rank : 4
Schlafli Type : {2,42,6}
Number of vertices, edges, etc : 2, 42, 126, 6
Order of s₀s₁s₂s₃ : 42
Order of s₀s₁s₂s₃s₂s₁ : 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 : {2,14,6}*336
   7-fold quotients : {2,6,6}*144b
   9-fold quotients : {2,14,2}*112
   14-fold quotients : {2,6,3}*72
   18-fold quotients : {2,7,2}*56
   21-fold quotients : {2,2,6}*48
   42-fold quotients : {2,2,3}*24
   63-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4, 9)( 5, 8)( 6, 7)(10,17)(11,23)(12,22)(13,21)(14,20)(15,19)(16,18)
(25,30)(26,29)(27,28)(31,38)(32,44)(33,43)(34,42)(35,41)(36,40)(37,39)(46,51)
(47,50)(48,49)(52,59)(53,65)(54,64)(55,63)(56,62)(57,61)(58,60);;
s2 := ( 3,11)( 4,10)( 5,16)( 6,15)( 7,14)( 8,13)( 9,12)(17,18)(19,23)(20,22)
(24,53)(25,52)(26,58)(27,57)(28,56)(29,55)(30,54)(31,46)(32,45)(33,51)(34,50)
(35,49)(36,48)(37,47)(38,60)(39,59)(40,65)(41,64)(42,63)(43,62)(44,61);;
s3 := ( 3,24)( 4,25)( 5,26)( 6,27)( 7,28)( 8,29)( 9,30)(10,38)(11,39)(12,40)
(13,41)(14,42)(15,43)(16,44)(17,31)(18,32)(19,33)(20,34)(21,35)(22,36)(23,37)
(52,59)(53,60)(54,61)(55,62)(56,63)(57,64)(58,65);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2, 
s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(65)!(1,2);
s1 := Sym(65)!( 4, 9)( 5, 8)( 6, 7)(10,17)(11,23)(12,22)(13,21)(14,20)(15,19)
(16,18)(25,30)(26,29)(27,28)(31,38)(32,44)(33,43)(34,42)(35,41)(36,40)(37,39)
(46,51)(47,50)(48,49)(52,59)(53,65)(54,64)(55,63)(56,62)(57,61)(58,60);
s2 := Sym(65)!( 3,11)( 4,10)( 5,16)( 6,15)( 7,14)( 8,13)( 9,12)(17,18)(19,23)
(20,22)(24,53)(25,52)(26,58)(27,57)(28,56)(29,55)(30,54)(31,46)(32,45)(33,51)
(34,50)(35,49)(36,48)(37,47)(38,60)(39,59)(40,65)(41,64)(42,63)(43,62)(44,61);
s3 := Sym(65)!( 3,24)( 4,25)( 5,26)( 6,27)( 7,28)( 8,29)( 9,30)(10,38)(11,39)
(12,40)(13,41)(14,42)(15,43)(16,44)(17,31)(18,32)(19,33)(20,34)(21,35)(22,36)
(23,37)(52,59)(53,60)(54,61)(55,62)(56,63)(57,64)(58,65);
poly := sub<Sym(65)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2, 
s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

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