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# Polytope of Type {10,2,3}

Atlas Canonical Name : {10,2,3}*120
if this polytope has a name.
Group : SmallGroup(120,42)
Rank : 4
Schlafli Type : {10,2,3}
Number of vertices, edges, etc : 10, 10, 3, 3
Order of s0s1s2s3 : 30
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{10,2,3,2} of size 240
{10,2,3,3} of size 480
{10,2,3,4} of size 480
{10,2,3,6} of size 720
{10,2,3,4} of size 960
{10,2,3,6} of size 960
{10,2,3,5} of size 1200
{10,2,3,8} of size 1920
{10,2,3,12} of size 1920
Vertex Figure Of :
{2,10,2,3} of size 240
{4,10,2,3} of size 480
{5,10,2,3} of size 600
{3,10,2,3} of size 720
{3,10,2,3} of size 720
{5,10,2,3} of size 720
{5,10,2,3} of size 720
{6,10,2,3} of size 720
{8,10,2,3} of size 960
{4,10,2,3} of size 1200
{10,10,2,3} of size 1200
{10,10,2,3} of size 1200
{10,10,2,3} of size 1200
{12,10,2,3} of size 1440
{4,10,2,3} of size 1440
{4,10,2,3} of size 1440
{6,10,2,3} of size 1440
{6,10,2,3} of size 1440
{3,10,2,3} of size 1440
{5,10,2,3} of size 1440
{6,10,2,3} of size 1440
{6,10,2,3} of size 1440
{6,10,2,3} of size 1440
{6,10,2,3} of size 1440
{10,10,2,3} of size 1440
{10,10,2,3} of size 1440
{10,10,2,3} of size 1440
{10,10,2,3} of size 1440
{14,10,2,3} of size 1680
{3,10,2,3} of size 1800
{6,10,2,3} of size 1800
{15,10,2,3} of size 1800
{16,10,2,3} of size 1920
{5,10,2,3} of size 1920
{4,10,2,3} of size 1920
{4,10,2,3} of size 1920
{5,10,2,3} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {5,2,3}*60
5-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
2-fold covers : {20,2,3}*240, {10,2,6}*240
3-fold covers : {10,2,9}*360, {10,6,3}*360, {30,2,3}*360
4-fold covers : {40,2,3}*480, {10,2,12}*480, {20,2,6}*480, {10,4,6}*480, {10,4,3}*480
5-fold covers : {50,2,3}*600, {10,2,15}*600
6-fold covers : {20,2,9}*720, {10,2,18}*720, {20,6,3}*720, {60,2,3}*720, {10,6,6}*720a, {10,6,6}*720b, {30,2,6}*720
7-fold covers : {10,2,21}*840, {70,2,3}*840
8-fold covers : {80,2,3}*960, {20,2,12}*960, {10,4,12}*960, {20,4,6}*960, {10,2,24}*960, {40,2,6}*960, {10,8,6}*960, {20,4,3}*960, {10,8,3}*960, {10,4,6}*960
9-fold covers : {10,2,27}*1080, {10,6,9}*1080, {10,6,3}*1080, {90,2,3}*1080, {30,2,9}*1080, {30,6,3}*1080a, {30,6,3}*1080b
10-fold covers : {100,2,3}*1200, {50,2,6}*1200, {20,2,15}*1200, {10,10,6}*1200a, {10,10,6}*1200c, {10,2,30}*1200
11-fold covers : {10,2,33}*1320, {110,2,3}*1320
12-fold covers : {40,2,9}*1440, {10,2,36}*1440, {20,2,18}*1440, {10,4,18}*1440, {40,6,3}*1440, {120,2,3}*1440, {10,4,9}*1440, {10,6,12}*1440a, {10,6,12}*1440b, {10,12,6}*1440a, {20,6,6}*1440a, {20,6,6}*1440c, {10,12,6}*1440c, {30,2,12}*1440, {60,2,6}*1440, {30,4,6}*1440, {10,6,3}*1440, {10,12,3}*1440, {30,4,3}*1440
13-fold covers : {10,2,39}*1560, {130,2,3}*1560
14-fold covers : {20,2,21}*1680, {140,2,3}*1680, {10,14,6}*1680, {10,2,42}*1680, {70,2,6}*1680
15-fold covers : {50,2,9}*1800, {50,6,3}*1800, {150,2,3}*1800, {10,2,45}*1800, {10,6,15}*1800, {30,2,15}*1800
16-fold covers : {160,2,3}*1920, {20,4,12}*1920, {10,8,12}*1920a, {20,8,6}*1920a, {10,4,24}*1920a, {40,4,6}*1920a, {10,8,12}*1920b, {20,8,6}*1920b, {10,4,24}*1920b, {40,4,6}*1920b, {10,4,12}*1920a, {20,4,6}*1920a, {40,2,12}*1920, {20,2,24}*1920, {10,16,6}*1920, {10,2,48}*1920, {80,2,6}*1920, {20,8,3}*1920, {20,4,3}*1920, {10,8,3}*1920, {40,4,3}*1920, {10,4,12}*1920b, {20,4,6}*1920b, {10,4,6}*1920, {10,4,12}*1920c, {10,8,6}*1920a, {10,8,6}*1920b
Permutation Representation (GAP) :
```s0 := ( 3, 4)( 5, 6)( 7, 8)( 9,10);;
s1 := ( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);;
s2 := (12,13);;
s3 := (11,12);;
poly := Group([s0,s1,s2,s3]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3*s2*s3, 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(13)!( 3, 4)( 5, 6)( 7, 8)( 9,10);
s1 := Sym(13)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);
s2 := Sym(13)!(12,13);
s3 := Sym(13)!(11,12);
poly := sub<Sym(13)|s0,s1,s2,s3>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

```

to this polytope