# Polytope of Type {3,6}

Atlas Canonical Name : {3,6}*576
Also Known As : {3,6}(4,4)if this polytope has another name.
Group : SmallGroup(576,5053)
Rank : 3
Schlafli Type : {3,6}
Number of vertices, edges, etc : 48, 144, 96
Order of s0s1s2 : 24
Order of s0s1s2s1 : 6
Special Properties :
Toroidal
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{3,6,2} of size 1152
Vertex Figure Of :
{2,3,6} of size 1152
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {3,6}*192
4-fold quotients : {3,6}*144
12-fold quotients : {3,6}*48
16-fold quotients : {3,6}*36
24-fold quotients : {3,3}*24
48-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
2-fold covers : {3,12}*1152a, {6,6}*1152a
3-fold covers : {9,6}*1728, {3,6}*1728
Permutation Representation (GAP) :
```s0 := ( 3, 4)( 5,12)( 6,11)( 7, 9)( 8,10)(13,14)(17,33)(18,34)(19,36)(20,35)
(21,44)(22,43)(23,41)(24,42)(25,39)(26,40)(27,38)(28,37)(29,46)(30,45)(31,47)
(32,48);;
s1 := ( 1,17)( 2,19)( 3,18)( 4,20)( 5,24)( 6,22)( 7,23)( 8,21)( 9,32)(10,30)
(11,31)(12,29)(13,28)(14,26)(15,27)(16,25)(34,35)(37,40)(41,48)(42,46)(43,47)
(44,45);;
s2 := ( 1,15)( 2,16)( 3,14)( 4,13)( 5, 6)(11,12)(17,31)(18,32)(19,30)(20,29)
(21,22)(27,28)(33,47)(34,48)(35,46)(36,45)(37,38)(43,44);;
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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope