Polytope of Type {2,2,33}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,33}*264
if this polytope has a name.
Group : SmallGroup(264,38)
Rank : 4
Schlafli Type : {2,2,33}
Number of vertices, edges, etc : 2, 2, 33, 33
Order of s₀s₁s₂s₃ : 66
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,33,2} of size 528
   {2,2,33,4} of size 1056
   {2,2,33,6} of size 1584
Vertex Figure Of :
   {2,2,2,33} of size 528
   {3,2,2,33} of size 792
   {4,2,2,33} of size 1056
   {5,2,2,33} of size 1320
   {6,2,2,33} of size 1584
   {7,2,2,33} of size 1848
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,2,11}*88
   11-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,2,33}*528, {2,2,66}*528
   3-fold covers : {2,2,99}*792, {2,6,33}*792, {6,2,33}*792
   4-fold covers : {8,2,33}*1056, {2,2,132}*1056, {2,4,66}*1056a, {4,2,66}*1056, {2,4,33}*1056
   5-fold covers : {10,2,33}*1320, {2,2,165}*1320
   6-fold covers : {4,2,99}*1584, {2,2,198}*1584, {12,2,33}*1584, {4,6,33}*1584, {2,6,66}*1584b, {2,6,66}*1584c, {6,2,66}*1584
   7-fold covers : {14,2,33}*1848, {2,2,231}*1848
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := ( 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)(36,37);;
s3 := ( 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)(35,36);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(37)!(1,2);
s1 := Sym(37)!(3,4);
s2 := Sym(37)!( 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)(36,37);
s3 := Sym(37)!( 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)(35,36);
poly := sub<Sym(37)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope