Polytope of Type {6,39}

Atlas Canonical Name : {6,39}*624
if this polytope has a name.
Group : SmallGroup(624,242)
Rank : 3
Schlafli Type : {6,39}
Number of vertices, edges, etc : 8, 156, 52
Order of s0s1s2 : 52
Order of s0s1s2s1 : 6
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{6,39,2} of size 1248
Vertex Figure Of :
{2,6,39} of size 1248
Quotients (Maximal Quotients in Boldface) :
12-fold quotients : {2,13}*52
13-fold quotients : {6,3}*48
26-fold quotients : {3,3}*24
Covers (Minimal Covers in Boldface) :
2-fold covers : {12,39}*1248, {6,78}*1248
3-fold covers : {6,39}*1872
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)(46,47)(50,51);;
s1 := ( 3, 4)( 5,49)( 6,50)( 7,52)( 8,51)( 9,45)(10,46)(11,48)(12,47)(13,41)
(14,42)(15,44)(16,43)(17,37)(18,38)(19,40)(20,39)(21,33)(22,34)(23,36)(24,35)
(25,29)(26,30)(27,32)(28,31);;
s2 := ( 1, 8)( 2, 6)( 3, 7)( 4, 5)( 9,52)(10,50)(11,51)(12,49)(13,48)(14,46)
(15,47)(16,45)(17,44)(18,42)(19,43)(20,41)(21,40)(22,38)(23,39)(24,37)(25,36)
(26,34)(27,35)(28,33)(29,32);;
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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2 ];;
poly := F / rels;;

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

```
References : None.
to this polytope