# Polytope of Type {2,15,6}

Atlas Canonical Name : {2,15,6}*360
if this polytope has a name.
Group : SmallGroup(360,154)
Rank : 4
Schlafli Type : {2,15,6}
Number of vertices, edges, etc : 2, 15, 45, 6
Order of s0s1s2s3 : 30
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,15,6,2} of size 720
{2,15,6,3} of size 1080
{2,15,6,4} of size 1440
Vertex Figure Of :
{2,2,15,6} of size 720
{3,2,15,6} of size 1080
{4,2,15,6} of size 1440
{5,2,15,6} of size 1800
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {2,15,2}*120
5-fold quotients : {2,3,6}*72
9-fold quotients : {2,5,2}*40
15-fold quotients : {2,3,2}*24
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,30,6}*720c
3-fold covers : {2,45,6}*1080, {2,15,6}*1080, {6,15,6}*1080
4-fold covers : {2,60,6}*1440c, {4,30,6}*1440c, {2,30,12}*1440c, {4,15,6}*1440b, {2,15,12}*1440, {2,15,6}*1440e
5-fold covers : {2,75,6}*1800, {10,15,6}*1800, {2,15,30}*1800
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 4, 7)( 5, 6)( 8,13)( 9,17)(10,16)(11,15)(12,14)(18,33)(19,37)(20,36)
(21,35)(22,34)(23,43)(24,47)(25,46)(26,45)(27,44)(28,38)(29,42)(30,41)(31,40)
(32,39);;
s2 := ( 3,24)( 4,23)( 5,27)( 6,26)( 7,25)( 8,19)( 9,18)(10,22)(11,21)(12,20)
(13,29)(14,28)(15,32)(16,31)(17,30)(33,39)(34,38)(35,42)(36,41)(37,40)(43,44)
(45,47);;
s3 := (18,33)(19,34)(20,35)(21,36)(22,37)(23,38)(24,39)(25,40)(26,41)(27,42)
(28,43)(29,44)(30,45)(31,46)(32,47);;
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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(47)!(1,2);
s1 := Sym(47)!( 4, 7)( 5, 6)( 8,13)( 9,17)(10,16)(11,15)(12,14)(18,33)(19,37)
(20,36)(21,35)(22,34)(23,43)(24,47)(25,46)(26,45)(27,44)(28,38)(29,42)(30,41)
(31,40)(32,39);
s2 := Sym(47)!( 3,24)( 4,23)( 5,27)( 6,26)( 7,25)( 8,19)( 9,18)(10,22)(11,21)
(12,20)(13,29)(14,28)(15,32)(16,31)(17,30)(33,39)(34,38)(35,42)(36,41)(37,40)
(43,44)(45,47);
s3 := Sym(47)!(18,33)(19,34)(20,35)(21,36)(22,37)(23,38)(24,39)(25,40)(26,41)
(27,42)(28,43)(29,44)(30,45)(31,46)(32,47);
poly := sub<Sym(47)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

```

to this polytope