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# Polytope of Type {9,9}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,9}*1152
if this polytope has a name.
Group : SmallGroup(1152,157853)
Rank : 3
Schlafli Type : {9,9}
Number of vertices, edges, etc : 64, 288, 64
Order of s0s1s2 : 4
Order of s0s1s2s1 : 9
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Dual
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) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := ( 3, 4)( 5,17)( 6,18)( 7,20)( 8,19)( 9,49)(10,50)(11,52)(12,51)(13,33)
(14,34)(15,36)(16,35)(23,24)(25,53)(26,54)(27,56)(28,55)(29,37)(30,38)(31,40)
(32,39)(41,61)(42,62)(43,64)(44,63)(47,48)(59,60);;
s1 := ( 2,33)( 3,49)( 4,17)( 6,37)( 7,53)( 8,21)( 9,13)(10,45)(11,61)(12,29)
(14,41)(15,57)(16,25)(18,36)(19,52)(22,40)(23,56)(26,48)(27,64)(28,32)(30,44)
(31,60)(35,50)(39,54)(42,46)(43,62)(47,58)(59,63);;
s2 := ( 1, 2)( 5,18)( 6,17)( 7,19)( 8,20)( 9,50)(10,49)(11,51)(12,52)(13,34)
(14,33)(15,35)(16,36)(21,22)(25,54)(26,53)(27,55)(28,56)(29,38)(30,37)(31,39)
(32,40)(41,62)(42,61)(43,63)(44,64)(45,46)(57,58);;
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*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(64)!( 3, 4)( 5,17)( 6,18)( 7,20)( 8,19)( 9,49)(10,50)(11,52)(12,51)
(13,33)(14,34)(15,36)(16,35)(23,24)(25,53)(26,54)(27,56)(28,55)(29,37)(30,38)
(31,40)(32,39)(41,61)(42,62)(43,64)(44,63)(47,48)(59,60);
s1 := Sym(64)!( 2,33)( 3,49)( 4,17)( 6,37)( 7,53)( 8,21)( 9,13)(10,45)(11,61)
(12,29)(14,41)(15,57)(16,25)(18,36)(19,52)(22,40)(23,56)(26,48)(27,64)(28,32)
(30,44)(31,60)(35,50)(39,54)(42,46)(43,62)(47,58)(59,63);
s2 := Sym(64)!( 1, 2)( 5,18)( 6,17)( 7,19)( 8,20)( 9,50)(10,49)(11,51)(12,52)
(13,34)(14,33)(15,35)(16,36)(21,22)(25,54)(26,53)(27,55)(28,56)(29,38)(30,37)
(31,39)(32,40)(41,62)(42,61)(43,63)(44,64)(45,46)(57,58);
poly := sub<Sym(64)|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*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1 >;

```
References : None.
to this polytope