# Polytope of Type {2,18,2,6}

Atlas Canonical Name : {2,18,2,6}*864
if this polytope has a name.
Group : SmallGroup(864,4032)
Rank : 5
Schlafli Type : {2,18,2,6}
Number of vertices, edges, etc : 2, 18, 18, 6, 6
Order of s0s1s2s3s4 : 18
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,18,2,6,2} of size 1728
Vertex Figure Of :
{2,2,18,2,6} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,9,2,6}*432, {2,18,2,3}*432
3-fold quotients : {2,18,2,2}*288, {2,6,2,6}*288
4-fold quotients : {2,9,2,3}*216
6-fold quotients : {2,9,2,2}*144, {2,3,2,6}*144, {2,6,2,3}*144
9-fold quotients : {2,2,2,6}*96, {2,6,2,2}*96
12-fold quotients : {2,3,2,3}*72
18-fold quotients : {2,2,2,3}*48, {2,3,2,2}*48
27-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,18,2,12}*1728, {2,36,2,6}*1728, {2,18,4,6}*1728, {4,18,2,6}*1728a
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20);;
s2 := ( 3, 7)( 4, 5)( 6,11)( 8, 9)(10,15)(12,13)(14,19)(16,17)(18,20);;
s3 := (23,24)(25,26);;
s4 := (21,25)(22,23)(24,26);;
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*s1*s0*s1,
s0*s2*s0*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, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(26)!(1,2);
s1 := Sym(26)!( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20);
s2 := Sym(26)!( 3, 7)( 4, 5)( 6,11)( 8, 9)(10,15)(12,13)(14,19)(16,17)(18,20);
s3 := Sym(26)!(23,24)(25,26);
s4 := Sym(26)!(21,25)(22,23)(24,26);
poly := sub<Sym(26)|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*s1*s0*s1, s0*s2*s0*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,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

```

to this polytope