Polytope of Type {2,2,21,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,21,6}*1008
if this polytope has a name.
Group : SmallGroup(1008,942)
Rank : 5
Schlafli Type : {2,2,21,6}
Number of vertices, edges, etc : 2, 2, 21, 63, 6
Order of s₀s₁s₂s₃s₄ : 42
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) :
   3-fold quotients : {2,2,21,2}*336
   7-fold quotients : {2,2,3,6}*144
   9-fold quotients : {2,2,7,2}*112
   21-fold quotients : {2,2,3,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6,11)( 7,10)( 8, 9)(12,19)(13,25)(14,24)(15,23)(16,22)(17,21)(18,20)
(26,47)(27,53)(28,52)(29,51)(30,50)(31,49)(32,48)(33,61)(34,67)(35,66)(36,65)
(37,64)(38,63)(39,62)(40,54)(41,60)(42,59)(43,58)(44,57)(45,56)(46,55);;
s3 := ( 5,34)( 6,33)( 7,39)( 8,38)( 9,37)(10,36)(11,35)(12,27)(13,26)(14,32)
(15,31)(16,30)(17,29)(18,28)(19,41)(20,40)(21,46)(22,45)(23,44)(24,43)(25,42)
(47,55)(48,54)(49,60)(50,59)(51,58)(52,57)(53,56)(61,62)(63,67)(64,66);;
s4 := (26,47)(27,48)(28,49)(29,50)(30,51)(31,52)(32,53)(33,54)(34,55)(35,56)
(36,57)(37,58)(38,59)(39,60)(40,61)(41,62)(42,63)(43,64)(44,65)(45,66)
(46,67);;
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*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, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, 
s2*s3*s4*s3*s2*s3*s2*s3*s4*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(67)!(1,2);
s1 := Sym(67)!(3,4);
s2 := Sym(67)!( 6,11)( 7,10)( 8, 9)(12,19)(13,25)(14,24)(15,23)(16,22)(17,21)
(18,20)(26,47)(27,53)(28,52)(29,51)(30,50)(31,49)(32,48)(33,61)(34,67)(35,66)
(36,65)(37,64)(38,63)(39,62)(40,54)(41,60)(42,59)(43,58)(44,57)(45,56)(46,55);
s3 := Sym(67)!( 5,34)( 6,33)( 7,39)( 8,38)( 9,37)(10,36)(11,35)(12,27)(13,26)
(14,32)(15,31)(16,30)(17,29)(18,28)(19,41)(20,40)(21,46)(22,45)(23,44)(24,43)
(25,42)(47,55)(48,54)(49,60)(50,59)(51,58)(52,57)(53,56)(61,62)(63,67)(64,66);
s4 := Sym(67)!(26,47)(27,48)(28,49)(29,50)(30,51)(31,52)(32,53)(33,54)(34,55)
(35,56)(36,57)(37,58)(38,59)(39,60)(40,61)(41,62)(42,63)(43,64)(44,65)(45,66)
(46,67);
poly := sub<Sym(67)|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*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, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s2*s3*s4*s3*s2*s3*s2*s3*s4*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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