Polytope of Type {2,66}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,66}*264
if this polytope has a name.
Group : SmallGroup(264,38)
Rank : 3
Schlafli Type : {2,66}
Number of vertices, edges, etc : 2, 66, 66
Order of s₀s₁s₂ : 66
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,66,2} of size 528
   {2,66,4} of size 1056
   {2,66,4} of size 1056
   {2,66,4} of size 1056
   {2,66,6} of size 1584
   {2,66,6} of size 1584
   {2,66,6} of size 1584
Vertex Figure Of :
   {2,2,66} of size 528
   {3,2,66} of size 792
   {4,2,66} of size 1056
   {5,2,66} of size 1320
   {6,2,66} of size 1584
   {7,2,66} of size 1848
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,33}*132
   3-fold quotients : {2,22}*88
   6-fold quotients : {2,11}*44
   11-fold quotients : {2,6}*24
   22-fold quotients : {2,3}*12
   33-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,132}*528, {4,66}*528a
   3-fold covers : {2,198}*792, {6,66}*792b, {6,66}*792c
   4-fold covers : {4,132}*1056a, {2,264}*1056, {8,66}*1056, {4,66}*1056
   5-fold covers : {10,66}*1320, {2,330}*1320
   6-fold covers : {2,396}*1584, {4,198}*1584a, {12,66}*1584b, {6,132}*1584b, {6,132}*1584c, {12,66}*1584c
   7-fold covers : {14,66}*1848, {2,462}*1848
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);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s1*s0*s1, s0*s2*s0*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*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)(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(68)!( 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);
poly := sub<Sym(68)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s1*s0*s1, s0*s2*s0*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*s1*s2 >;

to this polytope