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

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

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

```

to this polytope