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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {21,6,2,2}*1008
if this polytope has a name.
Group : SmallGroup(1008,942)
Rank : 5
Schlafli Type : {21,6,2,2}
Number of vertices, edges, etc : 21, 63, 6, 2, 2
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 : {21,2,2,2}*336
   7-fold quotients : {3,6,2,2}*144
   9-fold quotients : {7,2,2,2}*112
   21-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 7)( 3, 6)( 4, 5)( 8,15)( 9,21)(10,20)(11,19)(12,18)(13,17)(14,16)
(22,43)(23,49)(24,48)(25,47)(26,46)(27,45)(28,44)(29,57)(30,63)(31,62)(32,61)
(33,60)(34,59)(35,58)(36,50)(37,56)(38,55)(39,54)(40,53)(41,52)(42,51);;
s1 := ( 1,30)( 2,29)( 3,35)( 4,34)( 5,33)( 6,32)( 7,31)( 8,23)( 9,22)(10,28)
(11,27)(12,26)(13,25)(14,24)(15,37)(16,36)(17,42)(18,41)(19,40)(20,39)(21,38)
(43,51)(44,50)(45,56)(46,55)(47,54)(48,53)(49,52)(57,58)(59,63)(60,62);;
s2 := (22,43)(23,44)(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);;
s3 := (64,65);;
s4 := (66,67);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(67)!( 2, 7)( 3, 6)( 4, 5)( 8,15)( 9,21)(10,20)(11,19)(12,18)(13,17)
(14,16)(22,43)(23,49)(24,48)(25,47)(26,46)(27,45)(28,44)(29,57)(30,63)(31,62)
(32,61)(33,60)(34,59)(35,58)(36,50)(37,56)(38,55)(39,54)(40,53)(41,52)(42,51);
s1 := Sym(67)!( 1,30)( 2,29)( 3,35)( 4,34)( 5,33)( 6,32)( 7,31)( 8,23)( 9,22)
(10,28)(11,27)(12,26)(13,25)(14,24)(15,37)(16,36)(17,42)(18,41)(19,40)(20,39)
(21,38)(43,51)(44,50)(45,56)(46,55)(47,54)(48,53)(49,52)(57,58)(59,63)(60,62);
s2 := Sym(67)!(22,43)(23,44)(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);
s3 := Sym(67)!(64,65);
s4 := Sym(67)!(66,67);
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*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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