# Polytope of Type {12,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,10}*480c
if this polytope has a name.
Group : SmallGroup(480,956)
Rank : 3
Schlafli Type : {12,10}
Number of vertices, edges, etc : 24, 120, 20
Order of s0s1s2 : 20
Order of s0s1s2s1 : 10
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{12,10,2} of size 960
Vertex Figure Of :
{2,12,10} of size 960
{4,12,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {6,10}*240e
4-fold quotients : {3,10}*120a, {6,5}*120b
8-fold quotients : {3,5}*60
Covers (Minimal Covers in Boldface) :
2-fold covers : {24,10}*960c, {24,10}*960d, {12,10}*960c
3-fold covers : {12,10}*1440e
4-fold covers : {48,10}*1920c, {48,10}*1920d, {12,20}*1920g, {24,10}*1920d, {12,10}*1920c, {12,20}*1920l, {24,10}*1920f
Permutation Representation (GAP) :
```s0 := (2,3)(6,7)(8,9);;
s1 := (1,2)(3,4)(5,6)(8,9);;
s2 := (6,8)(7,9);;
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*s0*s1*s0*s1*s2*s1*s0*s1,
s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2,
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope