# Polytope of Type {30,10}

Atlas Canonical Name : {30,10}*1440
if this polytope has a name.
Group : SmallGroup(1440,5853)
Rank : 3
Schlafli Type : {30,10}
Number of vertices, edges, etc : 72, 360, 24
Order of s0s1s2 : 6
Order of s0s1s2s1 : 6
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {15,10}*720, {30,10}*720a, {30,10}*720b
3-fold quotients : {10,10}*480
4-fold quotients : {15,10}*360
6-fold quotients : {5,10}*240, {10,5}*240, {10,10}*240a, {10,10}*240b, {10,10}*240c, {10,10}*240d
12-fold quotients : {5,5}*120, {5,10}*120a, {5,10}*120b, {10,5}*120a, {10,5}*120b
24-fold quotients : {5,5}*60
60-fold quotients : {6,2}*24
120-fold quotients : {3,2}*12
180-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := ( 3, 6)( 4, 5)( 7,10)( 8, 9)(12,16)(13,15);;
s1 := ( 1, 3)( 2, 4)( 5, 8)( 6, 7)(11,12)(13,16)(14,15);;
s2 := ( 1, 2)( 3, 8)( 4, 7)( 5,10)( 6, 9);;
poly := Group([s0,s1,s2]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1,
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(16)!( 3, 6)( 4, 5)( 7,10)( 8, 9)(12,16)(13,15);
s1 := Sym(16)!( 1, 3)( 2, 4)( 5, 8)( 6, 7)(11,12)(13,16)(14,15);
s2 := Sym(16)!( 1, 2)( 3, 8)( 4, 7)( 5,10)( 6, 9);
poly := sub<Sym(16)|s0,s1,s2>;

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

```
References : None.
to this polytope