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# Polytope of Type {2,6,28,2}

Atlas Canonical Name : {2,6,28,2}*1344b
if this polytope has a name.
Group : SmallGroup(1344,11695)
Rank : 5
Schlafli Type : {2,6,28,2}
Number of vertices, edges, etc : 2, 6, 84, 28, 2
Order of s0s1s2s3s4 : 42
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-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 : {2,6,4,2}*192b
14-fold quotients : {2,3,4,2}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 4, 5)( 8, 9)(12,13)(16,17)(20,21)(24,25)(28,29);;
s2 := ( 5, 6)( 7,27)( 8,28)( 9,30)(10,29)(11,23)(12,24)(13,26)(14,25)(15,19)
(16,20)(17,22)(18,21);;
s3 := ( 3,10)( 4, 9)( 5, 8)( 6, 7)(11,30)(12,29)(13,28)(14,27)(15,26)(16,25)
(17,24)(18,23)(19,22)(20,21);;
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s3*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3 ];;
poly := F / rels;;

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

```

to this polytope