Polytope of Type {3,2,21,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,21,6}*1512
if this polytope has a name.
Group : SmallGroup(1512,838)
Rank : 5
Schlafli Type : {3,2,21,6}
Number of vertices, edges, etc : 3, 3, 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 : {3,2,21,2}*504
   7-fold quotients : {3,2,3,6}*216
   9-fold quotients : {3,2,7,2}*168
   21-fold quotients : {3,2,3,2}*72
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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