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# Polytope of Type {15,4,2}

Atlas Canonical Name : {15,4,2}*240
if this polytope has a name.
Group : SmallGroup(240,197)
Rank : 4
Schlafli Type : {15,4,2}
Number of vertices, edges, etc : 15, 30, 4, 2
Order of s0s1s2s3 : 30
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{15,4,2,2} of size 480
{15,4,2,3} of size 720
{15,4,2,4} of size 960
{15,4,2,5} of size 1200
{15,4,2,6} of size 1440
{15,4,2,7} of size 1680
{15,4,2,8} of size 1920
Vertex Figure Of :
{2,15,4,2} of size 480
{4,15,4,2} of size 960
{6,15,4,2} of size 1440
{4,15,4,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
5-fold quotients : {3,4,2}*48
Covers (Minimal Covers in Boldface) :
2-fold covers : {15,4,2}*480, {30,4,2}*480b, {30,4,2}*480c
3-fold covers : {45,4,2}*720
4-fold covers : {15,4,4}*960a, {60,4,2}*960b, {60,4,2}*960c, {15,4,4}*960b, {15,8,2}*960, {30,4,2}*960
5-fold covers : {75,4,2}*1200
6-fold covers : {45,4,2}*1440, {90,4,2}*1440b, {90,4,2}*1440c, {15,4,6}*1440, {15,12,2}*1440, {30,12,2}*1440d
7-fold covers : {105,4,2}*1680
8-fold covers : {15,4,4}*1920a, {15,4,4}*1920b, {30,4,4}*1920b, {30,4,4}*1920c, {30,4,2}*1920a, {15,8,2}*1920a, {30,8,2}*1920a, {15,8,4}*1920, {120,4,2}*1920c, {120,4,2}*1920d, {15,4,8}*1920, {60,4,2}*1920b, {30,4,4}*1920d, {30,4,2}*1920b, {60,4,2}*1920c, {30,8,2}*1920b, {30,8,2}*1920c
Permutation Representation (GAP) :
```s0 := ( 2, 3)( 5, 7)( 6, 8)( 9,10)(11,15)(12,14)(13,16)(17,19)(18,20);;
s1 := ( 1, 2)( 3, 5)( 4,13)( 6, 9)( 8,18)(10,14)(11,12)(15,17)(16,19);;
s2 := ( 1, 4)( 2, 6)( 3, 8)( 5,11)( 7,15)( 9,10)(12,16)(13,14)(17,20)(18,19);;
s3 := (21,22);;
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,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2, s2*s1*s0*s2*s1*s2*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*s0*s1*s0*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(22)!( 2, 3)( 5, 7)( 6, 8)( 9,10)(11,15)(12,14)(13,16)(17,19)(18,20);
s1 := Sym(22)!( 1, 2)( 3, 5)( 4,13)( 6, 9)( 8,18)(10,14)(11,12)(15,17)(16,19);
s2 := Sym(22)!( 1, 4)( 2, 6)( 3, 8)( 5,11)( 7,15)( 9,10)(12,16)(13,14)(17,20)
(18,19);
s3 := Sym(22)!(21,22);
poly := sub<Sym(22)|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, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2,
s2*s1*s0*s2*s1*s2*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*s0*s1*s0*s1 >;

```

to this polytope