Polytope of Type {33}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {33}*66
Also Known As : 33-gon, {33}. if this polytope has another name.
Group : SmallGroup(66,3)
Rank : 2
Schlafli Type : {33}
Number of vertices, edges, etc : 33, 33
Order of s₀s₁ : 33
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {33,2} of size 132
   {33,4} of size 264
   {33,6} of size 396
   {33,6} of size 528
   {33,4} of size 528
   {33,12} of size 1056
   {33,8} of size 1056
   {33,6} of size 1188
   {33,10} of size 1320
   {33,22} of size 1452
   {33,12} of size 1584
   {33,6} of size 1584
Vertex Figure Of :
   {2,33} of size 132
   {4,33} of size 264
   {6,33} of size 396
   {6,33} of size 528
   {4,33} of size 528
   {12,33} of size 1056
   {8,33} of size 1056
   {6,33} of size 1188
   {10,33} of size 1320
   {22,33} of size 1452
   {12,33} of size 1584
   {6,33} of size 1584
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {11}*22
   11-fold quotients : {3}*6
Covers (Minimal Covers in Boldface) :
   2-fold covers : {66}*132
   3-fold covers : {99}*198
   4-fold covers : {132}*264
   5-fold covers : {165}*330
   6-fold covers : {198}*396
   7-fold covers : {231}*462
   8-fold covers : {264}*528
   9-fold covers : {297}*594
   10-fold covers : {330}*660
   11-fold covers : {363}*726
   12-fold covers : {396}*792
   13-fold covers : {429}*858
   14-fold covers : {462}*924
   15-fold covers : {495}*990
   16-fold covers : {528}*1056
   17-fold covers : {561}*1122
   18-fold covers : {594}*1188
   19-fold covers : {627}*1254
   20-fold covers : {660}*1320
   21-fold covers : {693}*1386
   22-fold covers : {726}*1452
   23-fold covers : {759}*1518
   24-fold covers : {792}*1584
   25-fold covers : {825}*1650
   26-fold covers : {858}*1716
   27-fold covers : {891}*1782
   28-fold covers : {924}*1848
   29-fold covers : {957}*1914
   30-fold covers : {990}*1980
Permutation Representation (GAP) :

s0 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)
(22,23)(24,25)(26,27)(28,29)(30,31)(32,33);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)
(21,22)(23,24)(25,26)(27,28)(29,30)(31,32);;
poly := Group([s0,s1]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1");;
s0 := F.1;;  s1 := F.2;;  
rels := [ s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(33)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)
(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33);
s1 := Sym(33)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)
(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32);
poly := sub<Sym(33)|s0,s1>;

Finitely Presented Group Representation (Magma) :

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

References : None.
to this polytope