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# Polytope of Type {5,2,22,4}

Atlas Canonical Name : {5,2,22,4}*1760
if this polytope has a name.
Group : SmallGroup(1760,1190)
Rank : 5
Schlafli Type : {5,2,22,4}
Number of vertices, edges, etc : 5, 5, 22, 44, 4
Order of s0s1s2s3s4 : 220
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) :
2-fold quotients : {5,2,22,2}*880
4-fold quotients : {5,2,11,2}*440
11-fold quotients : {5,2,2,4}*160
22-fold quotients : {5,2,2,2}*80
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := ( 7,16)( 8,15)( 9,14)(10,13)(11,12)(18,27)(19,26)(20,25)(21,24)(22,23)
(29,38)(30,37)(31,36)(32,35)(33,34)(40,49)(41,48)(42,47)(43,46)(44,45);;
s3 := ( 6, 7)( 8,16)( 9,15)(10,14)(11,13)(17,18)(19,27)(20,26)(21,25)(22,24)
(28,40)(29,39)(30,49)(31,48)(32,47)(33,46)(34,45)(35,44)(36,43)(37,42)
(38,41);;
s4 := ( 6,28)( 7,29)( 8,30)( 9,31)(10,32)(11,33)(12,34)(13,35)(14,36)(15,37)
(16,38)(17,39)(18,40)(19,41)(20,42)(21,43)(22,44)(23,45)(24,46)(25,47)(26,48)
(27,49);;
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,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(49)!(2,3)(4,5);
s1 := Sym(49)!(1,2)(3,4);
s2 := Sym(49)!( 7,16)( 8,15)( 9,14)(10,13)(11,12)(18,27)(19,26)(20,25)(21,24)
(22,23)(29,38)(30,37)(31,36)(32,35)(33,34)(40,49)(41,48)(42,47)(43,46)(44,45);
s3 := Sym(49)!( 6, 7)( 8,16)( 9,15)(10,14)(11,13)(17,18)(19,27)(20,26)(21,25)
(22,24)(28,40)(29,39)(30,49)(31,48)(32,47)(33,46)(34,45)(35,44)(36,43)(37,42)
(38,41);
s4 := Sym(49)!( 6,28)( 7,29)( 8,30)( 9,31)(10,32)(11,33)(12,34)(13,35)(14,36)
(15,37)(16,38)(17,39)(18,40)(19,41)(20,42)(21,43)(22,44)(23,45)(24,46)(25,47)
(26,48)(27,49);
poly := sub<Sym(49)|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, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

```

to this polytope