Polytope of Type {2,33}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,33}*132
if this polytope has a name.
Group : SmallGroup(132,9)
Rank : 3
Schlafli Type : {2,33}
Number of vertices, edges, etc : 2, 33, 33
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 :
   {2,33,2} of size 264
   {2,33,4} of size 528
   {2,33,6} of size 792
   {2,33,6} of size 1056
   {2,33,4} of size 1056
Vertex Figure Of :
   {2,2,33} of size 264
   {3,2,33} of size 396
   {4,2,33} of size 528
   {5,2,33} of size 660
   {6,2,33} of size 792
   {7,2,33} of size 924
   {8,2,33} of size 1056
   {9,2,33} of size 1188
   {10,2,33} of size 1320
   {11,2,33} of size 1452
   {12,2,33} of size 1584
   {13,2,33} of size 1716
   {14,2,33} of size 1848
   {15,2,33} of size 1980
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,11}*44
   11-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,66}*264
   3-fold covers : {2,99}*396, {6,33}*396
   4-fold covers : {2,132}*528, {4,66}*528a, {4,33}*528
   5-fold covers : {2,165}*660
   6-fold covers : {2,198}*792, {6,66}*792b, {6,66}*792c
   7-fold covers : {2,231}*924
   8-fold covers : {4,132}*1056a, {2,264}*1056, {8,66}*1056, {8,33}*1056, {4,66}*1056
   9-fold covers : {2,297}*1188, {6,99}*1188, {6,33}*1188
   10-fold covers : {10,66}*1320, {2,330}*1320
   11-fold covers : {2,363}*1452, {22,33}*1452
   12-fold covers : {2,396}*1584, {4,198}*1584a, {4,99}*1584, {12,66}*1584b, {6,132}*1584b, {6,132}*1584c, {12,66}*1584c, {12,33}*1584, {6,33}*1584
   13-fold covers : {2,429}*1716
   14-fold covers : {14,66}*1848, {2,462}*1848
   15-fold covers : {2,495}*1980, {6,165}*1980
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 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)(34,35);;
s2 := ( 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)(33,34);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(35)!(1,2);
s1 := Sym(35)!( 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)(34,35);
s2 := Sym(35)!( 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)(33,34);
poly := sub<Sym(35)|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 >;

to this polytope