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# Polytope of Type {2,21,6,2}

Atlas Canonical Name : {2,21,6,2}*1344
if this polytope has a name.
Group : SmallGroup(1344,11695)
Rank : 5
Schlafli Type : {2,21,6,2}
Number of vertices, edges, etc : 2, 28, 84, 8, 2
Order of s0s1s2s3s4 : 28
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
7-fold quotients : {2,3,6,2}*192
12-fold quotients : {2,7,2,2}*112
14-fold quotients : {2,3,3,2}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 4, 5)( 7,27)( 8,29)( 9,28)(10,30)(11,23)(12,25)(13,24)(14,26)(15,19)
(16,21)(17,20)(18,22);;
s2 := ( 3, 7)( 4, 8)( 5,10)( 6, 9)(11,27)(12,28)(13,30)(14,29)(15,23)(16,24)
(17,26)(18,25)(21,22);;
s3 := ( 3, 6)( 7,10)(11,14)(15,18)(19,22)(23,26)(27,30);;
s4 := (31,32);;
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,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(32)!(1,2);
s1 := Sym(32)!( 4, 5)( 7,27)( 8,29)( 9,28)(10,30)(11,23)(12,25)(13,24)(14,26)
(15,19)(16,21)(17,20)(18,22);
s2 := Sym(32)!( 3, 7)( 4, 8)( 5,10)( 6, 9)(11,27)(12,28)(13,30)(14,29)(15,23)
(16,24)(17,26)(18,25)(21,22);
s3 := Sym(32)!( 3, 6)( 7,10)(11,14)(15,18)(19,22)(23,26)(27,30);
s4 := Sym(32)!(31,32);
poly := sub<Sym(32)|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, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 >;

```

to this polytope