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# Polytope of Type {3,2,3,10}

Atlas Canonical Name : {3,2,3,10}*720b
if this polytope has a name.
Group : SmallGroup(720,771)
Rank : 5
Schlafli Type : {3,2,3,10}
Number of vertices, edges, etc : 3, 3, 6, 30, 20
Order of s0s1s2s3s4 : 30
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{3,2,3,10,2} of size 1440
Vertex Figure Of :
{2,3,2,3,10} of size 1440
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {3,2,3,5}*360
Covers (Minimal Covers in Boldface) :
2-fold covers : {3,2,3,10}*1440, {3,2,6,10}*1440c, {3,2,6,10}*1440d, {6,2,3,10}*1440b
Permutation Representation (GAP) :
```s0 := (2,3);;
s1 := (1,2);;
s2 := ( 4, 6)( 5,11)( 7,15)( 8,10)( 9,12)(13,14);;
s3 := ( 4, 5)( 6,14)( 7, 8)( 9,15)(10,12)(11,13);;
s4 := ( 5,12)( 7,15)( 8,10)( 9,11);;
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,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s4*s2*s3*s4*s3*s4*s2*s3*s4*s3*s4 ];;
poly := F / rels;;

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

```

to this polytope