# Polytope of Type {52,6}

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

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

```
References : None.
to this polytope