Polytope of Type {2,6,21}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,21}*1512
if this polytope has a name.
Group : SmallGroup(1512,561)
Rank : 4
Schlafli Type : {2,6,21}
Number of vertices, edges, etc : 2, 18, 189, 63
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 : {2,6,21}*504
   7-fold quotients : {2,6,3}*216
   9-fold quotients : {2,2,21}*168
   21-fold quotients : {2,6,3}*72
   27-fold quotients : {2,2,7}*56
   63-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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