Polytope of Type {2,6,21}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,21}*504
if this polytope has a name.
Group : SmallGroup(504,192)
Rank : 4
Schlafli Type : {2,6,21}
Number of vertices, edges, etc : 2, 6, 63, 21
Order of s₀s₁s₂s₃ : 42
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,6,21,2} of size 1008
Vertex Figure Of :
   {2,2,6,21} of size 1008
   {3,2,6,21} of size 1512
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,2,21}*168
   7-fold quotients : {2,6,3}*72
   9-fold quotients : {2,2,7}*56
   21-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,6,21}*1008, {2,6,42}*1008c
   3-fold covers : {2,6,63}*1512, {2,6,21}*1512, {6,6,21}*1512b
Permutation Representation (GAP) :

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