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# Polytope of Type {15,2,4}

Atlas Canonical Name : {15,2,4}*240
if this polytope has a name.
Group : SmallGroup(240,179)
Rank : 4
Schlafli Type : {15,2,4}
Number of vertices, edges, etc : 15, 15, 4, 4
Order of s0s1s2s3 : 60
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{15,2,4,2} of size 480
{15,2,4,3} of size 720
{15,2,4,4} of size 960
{15,2,4,6} of size 1440
{15,2,4,3} of size 1440
{15,2,4,6} of size 1440
{15,2,4,6} of size 1440
{15,2,4,8} of size 1920
{15,2,4,8} of size 1920
{15,2,4,4} of size 1920
Vertex Figure Of :
{2,15,2,4} of size 480
{4,15,2,4} of size 960
{6,15,2,4} of size 1440
{6,15,2,4} of size 1920
{4,15,2,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {15,2,2}*120
3-fold quotients : {5,2,4}*80
5-fold quotients : {3,2,4}*48
6-fold quotients : {5,2,2}*40
10-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
2-fold covers : {15,2,8}*480, {30,2,4}*480
3-fold covers : {45,2,4}*720, {15,2,12}*720, {15,6,4}*720
4-fold covers : {15,2,16}*960, {60,2,4}*960, {30,4,4}*960, {30,2,8}*960, {15,4,4}*960b
5-fold covers : {75,2,4}*1200, {15,2,20}*1200, {15,10,4}*1200
6-fold covers : {45,2,8}*1440, {90,2,4}*1440, {15,2,24}*1440, {15,6,8}*1440, {30,2,12}*1440, {30,6,4}*1440b, {30,6,4}*1440c
7-fold covers : {15,2,28}*1680, {105,2,4}*1680
8-fold covers : {15,2,32}*1920, {60,4,4}*1920, {30,4,8}*1920a, {30,8,4}*1920a, {30,4,8}*1920b, {30,8,4}*1920b, {30,4,4}*1920a, {60,2,8}*1920, {120,2,4}*1920, {30,2,16}*1920, {15,8,4}*1920, {15,4,8}*1920, {30,4,4}*1920d
Permutation Representation (GAP) :
```s0 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14);;
s2 := (17,18);;
s3 := (16,17)(18,19);;
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*s2*s3, 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*s0*s1*s0*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(19)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15);
s1 := Sym(19)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14);
s2 := Sym(19)!(17,18);
s3 := Sym(19)!(16,17)(18,19);
poly := sub<Sym(19)|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*s2*s3,
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*s0*s1*s0*s1 >;

```

to this polytope