Polytope of Type {6,22,2,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,22,2,3}*1584
if this polytope has a name.
Group : SmallGroup(1584,675)
Rank : 5
Schlafli Type : {6,22,2,3}
Number of vertices, edges, etc : 6, 66, 22, 3, 3
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 : {2,22,2,3}*528
   6-fold quotients : {2,11,2,3}*264
   11-fold quotients : {6,2,2,3}*144
   22-fold quotients : {3,2,2,3}*72
   33-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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