Polytope of Type {2,2,6,22}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,6,22}*1056
if this polytope has a name.
Group : SmallGroup(1056,1022)
Rank : 5
Schlafli Type : {2,2,6,22}
Number of vertices, edges, etc : 2, 2, 6, 66, 22
Order of s₀s₁s₂s₃s₄ : 66
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 : {2,2,2,22}*352
   6-fold quotients : {2,2,2,11}*176
   11-fold quotients : {2,2,6,2}*96
   22-fold quotients : {2,2,3,2}*48
   33-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := (16,27)(17,28)(18,29)(19,30)(20,31)(21,32)(22,33)(23,34)(24,35)(25,36)
(26,37)(49,60)(50,61)(51,62)(52,63)(53,64)(54,65)(55,66)(56,67)(57,68)(58,69)
(59,70);;
s3 := ( 5,16)( 6,26)( 7,25)( 8,24)( 9,23)(10,22)(11,21)(12,20)(13,19)(14,18)
(15,17)(28,37)(29,36)(30,35)(31,34)(32,33)(38,49)(39,59)(40,58)(41,57)(42,56)
(43,55)(44,54)(45,53)(46,52)(47,51)(48,50)(61,70)(62,69)(63,68)(64,67)
(65,66);;
s4 := ( 5,39)( 6,38)( 7,48)( 8,47)( 9,46)(10,45)(11,44)(12,43)(13,42)(14,41)
(15,40)(16,50)(17,49)(18,59)(19,58)(20,57)(21,56)(22,55)(23,54)(24,53)(25,52)
(26,51)(27,61)(28,60)(29,70)(30,69)(31,68)(32,67)(33,66)(34,65)(35,64)(36,63)
(37,62);;
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, s2*s3*s4*s3*s2*s3*s4*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*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(70)!(1,2);
s1 := Sym(70)!(3,4);
s2 := Sym(70)!(16,27)(17,28)(18,29)(19,30)(20,31)(21,32)(22,33)(23,34)(24,35)
(25,36)(26,37)(49,60)(50,61)(51,62)(52,63)(53,64)(54,65)(55,66)(56,67)(57,68)
(58,69)(59,70);
s3 := Sym(70)!( 5,16)( 6,26)( 7,25)( 8,24)( 9,23)(10,22)(11,21)(12,20)(13,19)
(14,18)(15,17)(28,37)(29,36)(30,35)(31,34)(32,33)(38,49)(39,59)(40,58)(41,57)
(42,56)(43,55)(44,54)(45,53)(46,52)(47,51)(48,50)(61,70)(62,69)(63,68)(64,67)
(65,66);
s4 := Sym(70)!( 5,39)( 6,38)( 7,48)( 8,47)( 9,46)(10,45)(11,44)(12,43)(13,42)
(14,41)(15,40)(16,50)(17,49)(18,59)(19,58)(20,57)(21,56)(22,55)(23,54)(24,53)
(25,52)(26,51)(27,61)(28,60)(29,70)(30,69)(31,68)(32,67)(33,66)(34,65)(35,64)
(36,63)(37,62);
poly := sub<Sym(70)|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, 
s2*s3*s4*s3*s2*s3*s4*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*s3*s4 >;

to this polytope