Polytope of Type {4,33}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,33}*264
if this polytope has a name.
Group : SmallGroup(264,32)
Rank : 3
Schlafli Type : {4,33}
Number of vertices, edges, etc : 4, 66, 33
Order of s₀s₁s₂ : 33
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,33,2} of size 528
   {4,33,4} of size 1056
   {4,33,6} of size 1584
Vertex Figure Of :
   {2,4,33} of size 528
Quotients (Maximal Quotients in Boldface) :
   11-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,33}*528, {4,66}*528b, {4,66}*528c
   3-fold covers : {4,99}*792
   4-fold covers : {4,132}*1056b, {4,132}*1056c, {8,33}*1056, {4,66}*1056
   5-fold covers : {4,165}*1320
   6-fold covers : {4,99}*1584, {4,198}*1584b, {4,198}*1584c, {12,33}*1584, {12,66}*1584d
   7-fold covers : {4,231}*1848
Permutation Representation (GAP) :

s0 := ( 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)(33,34)(35,36)(37,38)(39,40)(41,42)
(43,44);;
s1 := ( 2, 3)( 5,41)( 6,43)( 7,42)( 8,44)( 9,37)(10,39)(11,38)(12,40)(13,33)
(14,35)(15,34)(16,36)(17,29)(18,31)(19,30)(20,32)(21,25)(22,27)(23,26)
(24,28);;
s2 := ( 1, 5)( 2, 6)( 3, 8)( 4, 7)( 9,41)(10,42)(11,44)(12,43)(13,37)(14,38)
(15,40)(16,39)(17,33)(18,34)(19,36)(20,35)(21,29)(22,30)(23,32)(24,31)
(27,28);;
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*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s0*s1, 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(44)!( 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)(33,34)(35,36)(37,38)(39,40)
(41,42)(43,44);
s1 := Sym(44)!( 2, 3)( 5,41)( 6,43)( 7,42)( 8,44)( 9,37)(10,39)(11,38)(12,40)
(13,33)(14,35)(15,34)(16,36)(17,29)(18,31)(19,30)(20,32)(21,25)(22,27)(23,26)
(24,28);
s2 := Sym(44)!( 1, 5)( 2, 6)( 3, 8)( 4, 7)( 9,41)(10,42)(11,44)(12,43)(13,37)
(14,38)(15,40)(16,39)(17,33)(18,34)(19,36)(20,35)(21,29)(22,30)(23,32)(24,31)
(27,28);
poly := sub<Sym(44)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

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

References : None.
to this polytope