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# Polytope of Type {3,2,2,13}

Atlas Canonical Name : {3,2,2,13}*312
if this polytope has a name.
Group : SmallGroup(312,54)
Rank : 5
Schlafli Type : {3,2,2,13}
Number of vertices, edges, etc : 3, 3, 2, 13, 13
Order of s0s1s2s3s4 : 78
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{3,2,2,13,2} of size 624
Vertex Figure Of :
{2,3,2,2,13} of size 624
{3,3,2,2,13} of size 1248
{4,3,2,2,13} of size 1248
{6,3,2,2,13} of size 1872
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {3,2,2,26}*624, {6,2,2,13}*624
3-fold covers : {9,2,2,13}*936, {3,6,2,13}*936, {3,2,2,39}*936
4-fold covers : {12,2,2,13}*1248, {3,2,2,52}*1248, {3,2,4,26}*1248, {6,4,2,13}*1248a, {3,4,2,13}*1248, {6,2,2,26}*1248
5-fold covers : {15,2,2,13}*1560, {3,2,2,65}*1560
6-fold covers : {9,2,2,26}*1872, {18,2,2,13}*1872, {3,2,6,26}*1872, {3,6,2,26}*1872, {6,6,2,13}*1872a, {6,6,2,13}*1872c, {3,2,2,78}*1872, {6,2,2,39}*1872
Permutation Representation (GAP) :
```s0 := (2,3);;
s1 := (1,2);;
s2 := (4,5);;
s3 := ( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18);;
s4 := ( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17);;
poly := Group([s0,s1,s2,s3,s4]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(18)!(2,3);
s1 := Sym(18)!(1,2);
s2 := Sym(18)!(4,5);
s3 := Sym(18)!( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18);
s4 := Sym(18)!( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17);
poly := sub<Sym(18)|s0,s1,s2,s3,s4>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

```

to this polytope