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# Polytope of Type {3,10}

Atlas Canonical Name : {3,10}*120b
if this polytope has a name.
Group : SmallGroup(120,35)
Rank : 3
Schlafli Type : {3,10}
Number of vertices, edges, etc : 6, 30, 20
Order of s0s1s2 : 10
Order of s0s1s2s1 : 10
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{3,10,2} of size 240
{3,10,4} of size 480
{3,10,6} of size 720
{3,10,8} of size 960
{3,10,10} of size 1200
{3,10,3} of size 1320
{3,10,12} of size 1440
{3,10,14} of size 1680
{3,10,16} of size 1920
{3,10,4} of size 1920
{3,10,4} of size 1920
Vertex Figure Of :
{2,3,10} of size 240
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {3,5}*60
Covers (Minimal Covers in Boldface) :
2-fold covers : {3,10}*240, {6,10}*240c, {6,10}*240d
4-fold covers : {6,20}*480a, {6,20}*480b, {3,20}*480, {6,10}*480c
6-fold covers : {3,10}*720b, {3,30}*720, {6,30}*720a
8-fold covers : {6,40}*960a, {6,40}*960b, {6,20}*960c, {12,10}*960c, {6,20}*960d, {12,10}*960d, {6,10}*960b
10-fold covers : {6,10}*1200a, {15,10}*1200a, {15,10}*1200b
12-fold covers : {6,60}*1440a, {6,60}*1440b, {3,20}*1440a, {3,60}*1440, {6,10}*1440f, {6,30}*1440e, {6,30}*1440f
14-fold covers : {6,70}*1680a, {21,10}*1680
16-fold covers : {6,80}*1920a, {6,80}*1920b, {12,20}*1920g, {6,40}*1920f, {24,10}*1920d, {6,20}*1920d, {12,10}*1920c, {12,20}*1920k, {12,20}*1920l, {12,20}*1920m, {6,40}*1920h, {24,10}*1920f, {6,10}*1920b
Permutation Representation (GAP) :
```s0 := ( 1, 3)( 2, 8)( 4,12)( 5, 7)( 6, 9)(10,11);;
s1 := ( 1, 2)( 3,11)( 4, 5)( 6,12)( 7, 9)( 8,10);;
s2 := ( 2, 9)( 4,12)( 5, 7)( 6, 8);;
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*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2 ];;
poly := F / rels;;

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

```
References : None.
to this polytope