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

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

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

Permutation Representation (Magma) :

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

to this polytope