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# Polytope of Type {6,33}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,33}*528
if this polytope has a name.
Group : SmallGroup(528,160)
Rank : 3
Schlafli Type : {6,33}
Number of vertices, edges, etc : 8, 132, 44
Order of s0s1s2 : 44
Order of s0s1s2s1 : 6
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{6,33,2} of size 1056
Vertex Figure Of :
{2,6,33} of size 1056
Quotients (Maximal Quotients in Boldface) :
11-fold quotients : {6,3}*48
12-fold quotients : {2,11}*44
22-fold quotients : {3,3}*24
Covers (Minimal Covers in Boldface) :
2-fold covers : {12,33}*1056, {6,66}*1056
3-fold covers : {6,33}*1584
Permutation Representation (GAP) :
```s0 := ( 2, 3)( 6, 7)(10,11)(14,15)(18,19)(22,23)(26,27)(30,31)(34,35)(38,39)
(42,43);;
s1 := ( 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);;
s2 := ( 1, 8)( 2, 6)( 3, 7)( 4, 5)( 9,44)(10,42)(11,43)(12,41)(13,40)(14,38)
(15,39)(16,37)(17,36)(18,34)(19,35)(20,33)(21,32)(22,30)(23,31)(24,29)
(25,28);;
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*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1,
s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope