# Polytope of Type {10,12}

Atlas Canonical Name : {10,12}*960c
if this polytope has a name.
Group : SmallGroup(960,10886)
Rank : 3
Schlafli Type : {10,12}
Number of vertices, edges, etc : 40, 240, 48
Order of s0s1s2 : 20
Order of s0s1s2s1 : 10
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{10,12,2} of size 1920
Vertex Figure Of :
{2,10,12} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {10,12}*480c, {10,12}*480d, {10,6}*480c
4-fold quotients : {5,6}*240b, {10,3}*240, {10,6}*240c, {10,6}*240d, {10,6}*240e, {10,6}*240f
8-fold quotients : {5,3}*120, {5,6}*120b, {5,6}*120c, {10,3}*120a, {10,3}*120b
16-fold quotients : {5,3}*60
60-fold quotients : {2,4}*16
120-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {20,12}*1920g, {10,24}*1920d, {10,12}*1920c, {20,12}*1920k, {10,24}*1920f
Permutation Representation (GAP) :
```s0 := ( 1, 2)( 8, 9)(10,11);;
s1 := ( 4, 6)( 7, 8)( 9,10);;
s2 := ( 3, 4)( 5, 6)( 8,11)( 9,10);;
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*s0*s1*s2*s1*s2*s1,
s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope