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Polytope of Type {20,8}

Atlas Canonical Name : {20,8}*1920c
if this polytope has a name.
Group : SmallGroup(1920,240844)
Rank : 3
Schlafli Type : {20,8}
Number of vertices, edges, etc : 120, 480, 48
Order of s0s1s2 : 12
Order of s0s1s2s1 : 6
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {10,8}*960c, {20,4}*960c
4-fold quotients : {5,8}*480, {10,4}*480c
8-fold quotients : {5,4}*240, {10,4}*240a, {10,4}*240b
16-fold quotients : {5,4}*120
120-fold quotients : {4,2}*16
240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := ( 1,15)( 2, 4)( 3,14)( 5, 9)( 6,31)( 7,35)( 8,24)(11,30)(12,18)(13,20)
(17,25)(19,32)(21,39)(22,40)(23,26)(29,34)(33,36)(37,38)(42,44);;
s1 := ( 1, 4)( 2, 7)( 3,10)( 5,13)( 8,19)( 9,21)(11,25)(12,27)(14,29)(15,26)
(16,32)(17,20)(18,22)(23,33)(28,37)(30,39)(31,38)(35,36)(41,44)(42,43);;
s2 := ( 1, 3)( 2,11)( 4,30)( 5,37)( 6,22)( 8,24)( 9,38)(10,28)(12,39)(13,33)
(14,15)(16,27)(17,25)(18,21)(19,26)(20,36)(23,32)(29,34)(31,40);;
poly := Group([s0,s1,s2]);;

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

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

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

```
References : None.
to this polytope