Polytope of Type {2,22,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,22,6}*528
if this polytope has a name.
Group : SmallGroup(528,164)
Rank : 4
Schlafli Type : {2,22,6}
Number of vertices, edges, etc : 2, 22, 66, 6
Order of s₀s₁s₂s₃ : 66
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,22,6,2} of size 1056
   {2,22,6,3} of size 1584
Vertex Figure Of :
   {2,2,22,6} of size 1056
   {3,2,22,6} of size 1584
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,22,2}*176
   6-fold quotients : {2,11,2}*88
   11-fold quotients : {2,2,6}*48
   22-fold quotients : {2,2,3}*24
   33-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,22,12}*1056, {2,44,6}*1056a, {4,22,6}*1056
   3-fold covers : {2,22,18}*1584, {6,22,6}*1584, {2,66,6}*1584a, {2,66,6}*1584b
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope