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Polytope of Type {6,6}

Atlas Canonical Name : {6,6}*1152e
if this polytope has a name.
Group : SmallGroup(1152,155791)
Rank : 3
Schlafli Type : {6,6}
Number of vertices, edges, etc : 96, 288, 96
Order of s0s1s2 : 24
Order of s0s1s2s1 : 6
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {6,6}*384e
4-fold quotients : {6,6}*288a
6-fold quotients : {3,6}*192
8-fold quotients : {6,3}*144
12-fold quotients : {6,6}*96
16-fold quotients : {6,6}*72b
24-fold quotients : {3,6}*48, {6,3}*48
32-fold quotients : {6,3}*36
48-fold quotients : {3,3}*24, {2,6}*24
96-fold quotients : {2,3}*12
144-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := ( 3, 4)( 5, 6)( 9,13)(10,14)(11,16)(12,15)(19,20)(21,22)(25,29)(26,30)
(27,32)(28,31)(35,36)(37,38)(41,45)(42,46)(43,48)(44,47);;
s1 := ( 2, 4)( 5,14)( 6,15)( 7,16)( 8,13)(10,12)(17,33)(18,36)(19,35)(20,34)
(21,46)(22,47)(23,48)(24,45)(25,41)(26,44)(27,43)(28,42)(29,40)(30,37)(31,38)
(32,39);;
s2 := ( 1,23)( 2,24)( 3,22)( 4,21)( 5,20)( 6,19)( 7,17)( 8,18)( 9,25)(10,26)
(11,28)(12,27)(13,29)(14,30)(15,32)(16,31)(33,39)(34,40)(35,38)(36,37)(43,44)
(47,48);;
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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1,
s2*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(48)!( 3, 4)( 5, 6)( 9,13)(10,14)(11,16)(12,15)(19,20)(21,22)(25,29)
(26,30)(27,32)(28,31)(35,36)(37,38)(41,45)(42,46)(43,48)(44,47);
s1 := Sym(48)!( 2, 4)( 5,14)( 6,15)( 7,16)( 8,13)(10,12)(17,33)(18,36)(19,35)
(20,34)(21,46)(22,47)(23,48)(24,45)(25,41)(26,44)(27,43)(28,42)(29,40)(30,37)
(31,38)(32,39);
s2 := Sym(48)!( 1,23)( 2,24)( 3,22)( 4,21)( 5,20)( 6,19)( 7,17)( 8,18)( 9,25)
(10,26)(11,28)(12,27)(13,29)(14,30)(15,32)(16,31)(33,39)(34,40)(35,38)(36,37)
(43,44)(47,48);
poly := sub<Sym(48)|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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1,
s2*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1 >;

```
References : None.
to this polytope