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# Polytope of Type {20,12}

Atlas Canonical Name : {20,12}*1920g
if this polytope has a name.
Group : SmallGroup(1920,240508)
Rank : 3
Schlafli Type : {20,12}
Number of vertices, edges, etc : 80, 480, 48
Order of s0s1s2 : 20
Order of s0s1s2s1 : 10
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Petrie
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 : {10,12}*960c, {20,6}*960c
4-fold quotients : {10,12}*480c, {10,12}*480d, {20,6}*480a, {20,6}*480b, {10,6}*480c
8-fold quotients : {5,6}*240b, {10,3}*240, {10,6}*240c, {10,6}*240d, {10,6}*240e, {10,6}*240f
16-fold quotients : {5,3}*120, {5,6}*120b, {5,6}*120c, {10,3}*120a, {10,3}*120b
32-fold quotients : {5,3}*60
60-fold quotients : {4,4}*32
120-fold quotients : {2,4}*16, {4,2}*16
240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := ( 1, 6)( 2, 8)( 3, 7)( 4, 5)(10,11)(12,13);;
s1 := ( 1, 8)( 2, 5)( 3, 4)( 6, 7)( 9,12)(10,13);;
s2 := ( 1, 6)( 2, 7)( 3, 8)( 4, 5)(10,13)(11,12);;
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, s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1,
s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(13)!( 1, 6)( 2, 8)( 3, 7)( 4, 5)(10,11)(12,13);
s1 := Sym(13)!( 1, 8)( 2, 5)( 3, 4)( 6, 7)( 9,12)(10,13);
s2 := Sym(13)!( 1, 6)( 2, 7)( 3, 8)( 4, 5)(10,13)(11,12);
poly := sub<Sym(13)|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, s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1,
s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

```
References : None.
to this polytope