Polytope of Type {2,33,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,33,2}*264
if this polytope has a name.
Group : SmallGroup(264,38)
Rank : 4
Schlafli Type : {2,33,2}
Number of vertices, edges, etc : 2, 33, 33, 2
Order of s₀s₁s₂s₃ : 66
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,33,2,2} of size 528
   {2,33,2,3} of size 792
   {2,33,2,4} of size 1056
   {2,33,2,5} of size 1320
   {2,33,2,6} of size 1584
   {2,33,2,7} of size 1848
Vertex Figure Of :
   {2,2,33,2} of size 528
   {3,2,33,2} of size 792
   {4,2,33,2} of size 1056
   {5,2,33,2} of size 1320
   {6,2,33,2} of size 1584
   {7,2,33,2} of size 1848
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,11,2}*88
   11-fold quotients : {2,3,2}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,66,2}*528
   3-fold covers : {2,99,2}*792, {2,33,6}*792, {6,33,2}*792
   4-fold covers : {2,132,2}*1056, {2,66,4}*1056a, {4,66,2}*1056a, {2,33,4}*1056, {4,33,2}*1056
   5-fold covers : {2,165,2}*1320
   6-fold covers : {2,198,2}*1584, {2,66,6}*1584b, {2,66,6}*1584c, {6,66,2}*1584b, {6,66,2}*1584c
   7-fold covers : {2,231,2}*1848
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);;
s3 := (36,37);;
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, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(37)!(1,2);
s1 := Sym(37)!( 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(37)!( 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);
s3 := Sym(37)!(36,37);
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, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

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