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# Polytope of Type {10,3}

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

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

```
References : None.
to this polytope