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# Polytope of Type {3,5,2,3}

Atlas Canonical Name : {3,5,2,3}*360
if this polytope has a name.
Group : SmallGroup(360,121)
Rank : 5
Schlafli Type : {3,5,2,3}
Number of vertices, edges, etc : 6, 15, 10, 3, 3
Order of s0s1s2s3s4 : 15
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{3,5,2,3,2} of size 720
{3,5,2,3,3} of size 1440
{3,5,2,3,4} of size 1440
Vertex Figure Of :
{2,3,5,2,3} of size 720
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {3,5,2,3}*720, {3,5,2,6}*720, {3,10,2,3}*720a, {3,10,2,3}*720b, {6,5,2,3}*720b, {6,5,2,3}*720c
3-fold covers : {3,5,2,9}*1080
4-fold covers : {3,5,2,12}*1440, {3,5,2,6}*1440, {3,10,2,3}*1440, {3,10,2,6}*1440a, {3,10,2,6}*1440b, {6,5,2,3}*1440b, {6,5,2,6}*1440b, {6,5,2,6}*1440c, {6,10,2,3}*1440c, {6,10,2,3}*1440d, {6,10,2,3}*1440e, {6,10,2,3}*1440f
5-fold covers : {3,5,2,15}*1800
Permutation Representation (GAP) :
```s0 := (2,3)(4,5);;
s1 := (1,2)(4,5);;
s2 := (2,4)(3,5);;
s3 := (7,8);;
s4 := (6,7);;
poly := Group([s0,s1,s2,s3,s4]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(8)!(2,3)(4,5);
s1 := Sym(8)!(1,2)(4,5);
s2 := Sym(8)!(2,4)(3,5);
s3 := Sym(8)!(7,8);
s4 := Sym(8)!(6,7);
poly := sub<Sym(8)|s0,s1,s2,s3,s4>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1,
s3*s4*s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2 >;

```

to this polytope