Questions?
See the FAQ
or other info.

# Polytope of Type {3,10}

Atlas Canonical Name : {3,10}*360
if this polytope has a name.
Group : SmallGroup(360,121)
Rank : 3
Schlafli Type : {3,10}
Number of vertices, edges, etc : 18, 90, 60
Order of s0s1s2 : 15
Order of s0s1s2s1 : 10
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{3,10,2} of size 720
Vertex Figure Of :
{2,3,10} of size 720
{4,3,10} of size 1440
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {3,10}*120a
6-fold quotients : {3,5}*60
Covers (Minimal Covers in Boldface) :
2-fold covers : {3,10}*720b, {6,10}*720b, {6,10}*720c
3-fold covers : {9,10}*1080
4-fold covers : {12,10}*1440e, {12,10}*1440f, {3,20}*1440a, {3,20}*1440b, {6,10}*1440f
5-fold covers : {15,10}*1800a
Permutation Representation (GAP) :
```s0 := (2,3)(5,6)(7,8);;
s1 := (1,2)(4,5)(7,8);;
s2 := (5,7)(6,8);;
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, 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,
s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

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

```
References : None.
to this polytope