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Polytope of Type {2,6,42}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,42}*1008a
if this polytope has a name.
Group : SmallGroup(1008,922)
Rank : 4
Schlafli Type : {2,6,42}
Number of vertices, edges, etc : 2, 6, 126, 42
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 : {2,6,14}*336
   7-fold quotients : {2,6,6}*144c
   9-fold quotients : {2,2,14}*112
   14-fold quotients : {2,3,6}*72
   18-fold quotients : {2,2,7}*56
   21-fold quotients : {2,6,2}*48
   42-fold quotients : {2,3,2}*24
   63-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (10,17)(11,18)(12,19)(13,20)(14,21)(15,22)(16,23)(24,45)(25,46)(26,47)
(27,48)(28,49)(29,50)(30,51)(31,59)(32,60)(33,61)(34,62)(35,63)(36,64)(37,65)
(38,52)(39,53)(40,54)(41,55)(42,56)(43,57)(44,58);;
s2 := ( 3,31)( 4,37)( 5,36)( 6,35)( 7,34)( 8,33)( 9,32)(10,24)(11,30)(12,29)
(13,28)(14,27)(15,26)(16,25)(17,38)(18,44)(19,43)(20,42)(21,41)(22,40)(23,39)
(45,52)(46,58)(47,57)(48,56)(49,55)(50,54)(51,53)(60,65)(61,64)(62,63);;
s3 := ( 3, 4)( 5, 9)( 6, 8)(10,18)(11,17)(12,23)(13,22)(14,21)(15,20)(16,19)
(24,25)(26,30)(27,29)(31,39)(32,38)(33,44)(34,43)(35,42)(36,41)(37,40)(45,46)
(47,51)(48,50)(52,60)(53,59)(54,65)(55,64)(56,63)(57,62)(58,61);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(65)!(1,2);
s1 := Sym(65)!(10,17)(11,18)(12,19)(13,20)(14,21)(15,22)(16,23)(24,45)(25,46)
(26,47)(27,48)(28,49)(29,50)(30,51)(31,59)(32,60)(33,61)(34,62)(35,63)(36,64)
(37,65)(38,52)(39,53)(40,54)(41,55)(42,56)(43,57)(44,58);
s2 := Sym(65)!( 3,31)( 4,37)( 5,36)( 6,35)( 7,34)( 8,33)( 9,32)(10,24)(11,30)
(12,29)(13,28)(14,27)(15,26)(16,25)(17,38)(18,44)(19,43)(20,42)(21,41)(22,40)
(23,39)(45,52)(46,58)(47,57)(48,56)(49,55)(50,54)(51,53)(60,65)(61,64)(62,63);
s3 := Sym(65)!( 3, 4)( 5, 9)( 6, 8)(10,18)(11,17)(12,23)(13,22)(14,21)(15,20)
(16,19)(24,25)(26,30)(27,29)(31,39)(32,38)(33,44)(34,43)(35,42)(36,41)(37,40)
(45,46)(47,51)(48,50)(52,60)(53,59)(54,65)(55,64)(56,63)(57,62)(58,61);
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2 >; 
 

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