Polytope of Type {33,4}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope