# Polytope of Type {6,33}

Atlas Canonical Name : {6,33}*396
if this polytope has a name.
Group : SmallGroup(396,22)
Rank : 3
Schlafli Type : {6,33}
Number of vertices, edges, etc : 6, 99, 33
Order of s0s1s2 : 66
Order of s0s1s2s1 : 6
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{6,33,2} of size 792
{6,33,4} of size 1584
Vertex Figure Of :
{2,6,33} of size 792
{3,6,33} of size 1188
{4,6,33} of size 1584
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {2,33}*132
9-fold quotients : {2,11}*44
11-fold quotients : {6,3}*36
33-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
2-fold covers : {6,66}*792c
3-fold covers : {6,99}*1188, {6,33}*1188
4-fold covers : {6,132}*1584c, {12,66}*1584c, {12,33}*1584, {6,33}*1584
5-fold covers : {6,165}*1980
Permutation Representation (GAP) :
```s0 := (34,67)(35,68)(36,69)(37,70)(38,71)(39,72)(40,73)(41,74)(42,75)(43,76)
(44,77)(45,78)(46,79)(47,80)(48,81)(49,82)(50,83)(51,84)(52,85)(53,86)(54,87)
(55,88)(56,89)(57,90)(58,91)(59,92)(60,93)(61,94)(62,95)(63,96)(64,97)(65,98)
(66,99);;
s1 := ( 1,34)( 2,44)( 3,43)( 4,42)( 5,41)( 6,40)( 7,39)( 8,38)( 9,37)(10,36)
(11,35)(12,56)(13,66)(14,65)(15,64)(16,63)(17,62)(18,61)(19,60)(20,59)(21,58)
(22,57)(23,45)(24,55)(25,54)(26,53)(27,52)(28,51)(29,50)(30,49)(31,48)(32,47)
(33,46)(68,77)(69,76)(70,75)(71,74)(72,73)(78,89)(79,99)(80,98)(81,97)(82,96)
(83,95)(84,94)(85,93)(86,92)(87,91)(88,90);;
s2 := ( 1,13)( 2,12)( 3,22)( 4,21)( 5,20)( 6,19)( 7,18)( 8,17)( 9,16)(10,15)
(11,14)(23,24)(25,33)(26,32)(27,31)(28,30)(34,79)(35,78)(36,88)(37,87)(38,86)
(39,85)(40,84)(41,83)(42,82)(43,81)(44,80)(45,68)(46,67)(47,77)(48,76)(49,75)
(50,74)(51,73)(52,72)(53,71)(54,70)(55,69)(56,90)(57,89)(58,99)(59,98)(60,97)
(61,96)(62,95)(63,94)(64,93)(65,92)(66,91);;
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, s2*s0*s1*s0*s1*s2*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(99)!(34,67)(35,68)(36,69)(37,70)(38,71)(39,72)(40,73)(41,74)(42,75)
(43,76)(44,77)(45,78)(46,79)(47,80)(48,81)(49,82)(50,83)(51,84)(52,85)(53,86)
(54,87)(55,88)(56,89)(57,90)(58,91)(59,92)(60,93)(61,94)(62,95)(63,96)(64,97)
(65,98)(66,99);
s1 := Sym(99)!( 1,34)( 2,44)( 3,43)( 4,42)( 5,41)( 6,40)( 7,39)( 8,38)( 9,37)
(10,36)(11,35)(12,56)(13,66)(14,65)(15,64)(16,63)(17,62)(18,61)(19,60)(20,59)
(21,58)(22,57)(23,45)(24,55)(25,54)(26,53)(27,52)(28,51)(29,50)(30,49)(31,48)
(32,47)(33,46)(68,77)(69,76)(70,75)(71,74)(72,73)(78,89)(79,99)(80,98)(81,97)
(82,96)(83,95)(84,94)(85,93)(86,92)(87,91)(88,90);
s2 := Sym(99)!( 1,13)( 2,12)( 3,22)( 4,21)( 5,20)( 6,19)( 7,18)( 8,17)( 9,16)
(10,15)(11,14)(23,24)(25,33)(26,32)(27,31)(28,30)(34,79)(35,78)(36,88)(37,87)
(38,86)(39,85)(40,84)(41,83)(42,82)(43,81)(44,80)(45,68)(46,67)(47,77)(48,76)
(49,75)(50,74)(51,73)(52,72)(53,71)(54,70)(55,69)(56,90)(57,89)(58,99)(59,98)
(60,97)(61,96)(62,95)(63,94)(64,93)(65,92)(66,91);
poly := sub<Sym(99)|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, s2*s0*s1*s0*s1*s2*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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