# Polytope of Type {5,6,2,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,6,2,3}*720b
if this polytope has a name.
Group : SmallGroup(720,771)
Rank : 5
Schlafli Type : {5,6,2,3}
Number of vertices, edges, etc : 10, 30, 12, 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 :
{5,6,2,3,2} of size 1440
Vertex Figure Of :
{2,5,6,2,3} of size 1440
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {5,3,2,3}*360
Covers (Minimal Covers in Boldface) :
2-fold covers : {5,6,2,3}*1440b, {5,6,2,6}*1440b, {10,6,2,3}*1440e, {10,6,2,3}*1440f
Permutation Representation (GAP) :
```s0 := ( 2, 9)( 4,12)( 5, 7)( 6, 8);;
s1 := ( 3, 5)( 4,11)( 6,12)( 7, 9);;
s2 := ( 1,11)( 2, 9)( 3,10)( 4, 5)( 6, 8)( 7,12);;
s3 := (14,15);;
s4 := (13,14);;
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,
s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(15)!( 2, 9)( 4,12)( 5, 7)( 6, 8);
s1 := Sym(15)!( 3, 5)( 4,11)( 6,12)( 7, 9);
s2 := Sym(15)!( 1,11)( 2, 9)( 3,10)( 4, 5)( 6, 8)( 7,12);
s3 := Sym(15)!(14,15);
s4 := Sym(15)!(13,14);
poly := sub<Sym(15)|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, s3*s4*s3*s4*s3*s4,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1 >;

```

to this polytope