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# Polytope of Type {3,6}

Atlas Canonical Name : {3,6}*300
Also Known As : {3,6}(5,0), {3,6}10if this polytope has another name.
Group : SmallGroup(300,25)
Rank : 3
Schlafli Type : {3,6}
Number of vertices, edges, etc : 25, 75, 50
Order of s0s1s2 : 10
Order of s0s1s2s1 : 6
Special Properties :
Toroidal
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{3,6,2} of size 600
{3,6,4} of size 1200
{3,6,6} of size 1800
Vertex Figure Of :
{2,3,6} of size 600
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {6,6}*600b
3-fold covers : {3,6}*900
4-fold covers : {12,6}*1200a, {6,12}*1200b, {3,6}*1200
5-fold covers : {3,30}*1500, {15,6}*1500a, {15,6}*1500b
6-fold covers : {6,6}*1800a, {6,6}*1800d
Permutation Representation (GAP) :
```s0 := ( 6,23)( 7,24)( 8,25)( 9,21)(10,22)(11,20)(12,16)(13,17)(14,18)(15,19);;
s1 := ( 2, 7)( 3,13)( 4,19)( 5,25)( 6,21)( 9,14)(10,20)(11,16)(12,22)(18,23);;
s2 := ( 1, 2)( 3, 5)( 6,10)( 7, 9)(11,13)(14,15)(17,20)(18,19)(21,24)(22,23);;
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*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(25)!( 6,23)( 7,24)( 8,25)( 9,21)(10,22)(11,20)(12,16)(13,17)(14,18)
(15,19);
s1 := Sym(25)!( 2, 7)( 3,13)( 4,19)( 5,25)( 6,21)( 9,14)(10,20)(11,16)(12,22)
(18,23);
s2 := Sym(25)!( 1, 2)( 3, 5)( 6,10)( 7, 9)(11,13)(14,15)(17,20)(18,19)(21,24)
(22,23);
poly := sub<Sym(25)|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*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;

```
References : None.
to this polytope