Polytope of Type {2,66,2,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,66,2,3}*1584
if this polytope has a name.
Group : SmallGroup(1584,688)
Rank : 5
Schlafli Type : {2,66,2,3}
Number of vertices, edges, etc : 2, 66, 66, 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) :
   2-fold quotients : {2,33,2,3}*792
   3-fold quotients : {2,22,2,3}*528
   6-fold quotients : {2,11,2,3}*264
   11-fold quotients : {2,6,2,3}*144
   22-fold quotients : {2,3,2,3}*72
   33-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4,13)( 5,12)( 6,11)( 7,10)( 8, 9)(14,25)(15,35)(16,34)(17,33)(18,32)
(19,31)(20,30)(21,29)(22,28)(23,27)(24,26)(37,46)(38,45)(39,44)(40,43)(41,42)
(47,58)(48,68)(49,67)(50,66)(51,65)(52,64)(53,63)(54,62)(55,61)(56,60)
(57,59);;
s2 := ( 3,48)( 4,47)( 5,57)( 6,56)( 7,55)( 8,54)( 9,53)(10,52)(11,51)(12,50)
(13,49)(14,37)(15,36)(16,46)(17,45)(18,44)(19,43)(20,42)(21,41)(22,40)(23,39)
(24,38)(25,59)(26,58)(27,68)(28,67)(29,66)(30,65)(31,64)(32,63)(33,62)(34,61)
(35,60);;
s3 := (70,71);;
s4 := (69,70);;
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, 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, 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*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*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(71)!(1,2);
s1 := Sym(71)!( 4,13)( 5,12)( 6,11)( 7,10)( 8, 9)(14,25)(15,35)(16,34)(17,33)
(18,32)(19,31)(20,30)(21,29)(22,28)(23,27)(24,26)(37,46)(38,45)(39,44)(40,43)
(41,42)(47,58)(48,68)(49,67)(50,66)(51,65)(52,64)(53,63)(54,62)(55,61)(56,60)
(57,59);
s2 := Sym(71)!( 3,48)( 4,47)( 5,57)( 6,56)( 7,55)( 8,54)( 9,53)(10,52)(11,51)
(12,50)(13,49)(14,37)(15,36)(16,46)(17,45)(18,44)(19,43)(20,42)(21,41)(22,40)
(23,39)(24,38)(25,59)(26,58)(27,68)(28,67)(29,66)(30,65)(31,64)(32,63)(33,62)
(34,61)(35,60);
s3 := Sym(71)!(70,71);
s4 := Sym(71)!(69,70);
poly := sub<Sym(71)|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, 
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, 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*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*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