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# Polytope of Type {2,4,20}

Atlas Canonical Name : {2,4,20}*1440
if this polytope has a name.
Group : SmallGroup(1440,5890)
Rank : 4
Schlafli Type : {2,4,20}
Number of vertices, edges, etc : 2, 18, 180, 90
Order of s0s1s2s3 : 30
Order of s0s1s2s3s2s1 : 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) :
5-fold quotients : {2,4,4}*288
10-fold quotients : {2,4,4}*144
18-fold quotients : {2,2,10}*80
36-fold quotients : {2,2,5}*40
90-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 8,38)( 9,39)(10,40)(11,41)(12,42)(13,28)(14,29)(15,30)(16,31)(17,32)
(18,33)(19,34)(20,35)(21,36)(22,37);;
s2 := ( 4, 7)( 5, 6)( 9,12)(10,11)(14,17)(15,16)(18,43)(19,47)(20,46)(21,45)
(22,44)(23,33)(24,37)(25,36)(26,35)(27,34)(28,38)(29,42)(30,41)(31,40)
(32,39);;
s3 := ( 3,24)( 4,23)( 5,27)( 6,26)( 7,25)( 8,34)( 9,33)(10,37)(11,36)(12,35)
(13,14)(15,17)(18,39)(19,38)(20,42)(21,41)(22,40)(28,29)(30,32)(43,44)
(45,47);;
poly := Group([s0,s1,s2,s3]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2,
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2,
s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s1 ];;
poly := F / rels;;

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

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2,
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2,
s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s1 >;

```

to this polytope