Polytope of Type {2,2,42,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,42,2,2}*1344
if this polytope has a name.
Group : SmallGroup(1344,11719)
Rank : 6
Schlafli Type : {2,2,42,2,2}
Number of vertices, edges, etc : 2, 2, 42, 42, 2, 2
Order of s0s1s2s3s4s5 : 42
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
   Self-Dual
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 : {2,2,21,2,2}*672
   3-fold quotients : {2,2,14,2,2}*448
   6-fold quotients : {2,2,7,2,2}*224
   7-fold quotients : {2,2,6,2,2}*192
   14-fold quotients : {2,2,3,2,2}*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 := ( 7, 8)( 9,10)(11,12)(13,14)(15,18)(16,17)(19,20)(21,24)(22,23)(25,26)
(27,30)(28,29)(31,32)(33,36)(34,35)(37,38)(39,42)(40,41)(43,46)(44,45);;
s3 := ( 5,21)( 6,15)( 7,13)( 8,23)( 9,11)(10,33)(12,17)(14,27)(16,25)(18,35)
(19,22)(20,43)(24,29)(26,39)(28,37)(30,45)(31,34)(32,44)(36,41)(38,40)
(42,46);;
s4 := (47,48);;
s5 := (49,50);;
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, s3*s4*s3*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(50)!(1,2);
s1 := Sym(50)!(3,4);
s2 := Sym(50)!( 7, 8)( 9,10)(11,12)(13,14)(15,18)(16,17)(19,20)(21,24)(22,23)
(25,26)(27,30)(28,29)(31,32)(33,36)(34,35)(37,38)(39,42)(40,41)(43,46)(44,45);
s3 := Sym(50)!( 5,21)( 6,15)( 7,13)( 8,23)( 9,11)(10,33)(12,17)(14,27)(16,25)
(18,35)(19,22)(20,43)(24,29)(26,39)(28,37)(30,45)(31,34)(32,44)(36,41)(38,40)
(42,46);
s4 := Sym(50)!(47,48);
s5 := Sym(50)!(49,50);
poly := sub<Sym(50)|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, 
s3*s4*s3*s4, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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