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# Polytope of Type {8,10}

Atlas Canonical Name : {8,10}*960c
if this polytope has a name.
Group : SmallGroup(960,10869)
Rank : 3
Schlafli Type : {8,10}
Number of vertices, edges, etc : 48, 240, 60
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 :
{8,10,2} of size 1920
Vertex Figure Of :
{2,8,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {8,5}*480, {4,10}*480c
4-fold quotients : {4,5}*240, {4,10}*240a, {4,10}*240b
8-fold quotients : {4,5}*120
120-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {8,10}*1920b, {8,20}*1920c, {8,20}*1920d
Permutation Representation (GAP) :
```s0 := ( 5, 6)( 7,20)( 8,19)( 9,21)(10,22)(11,13)(12,14)(15,37)(16,38)(17,35)
(18,36)(23,24)(27,32)(28,31)(29,34)(30,33)(39,40);;
s1 := ( 3,11)( 4,12)( 5,14)( 6,13)( 7,40)( 8,39)( 9,41)(10,42)(15,34)(16,33)
(17,32)(18,31)(19,25)(20,26)(21,23)(22,24)(27,28)(29,30);;
s2 := ( 1, 2)( 3,25)( 4,26)( 5,24)( 6,23)( 7,16)( 8,15)( 9,17)(10,18)(19,37)
(20,38)(21,35)(22,36)(27,33)(28,34)(29,31)(30,32)(39,40)(41,42);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*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(42)!( 5, 6)( 7,20)( 8,19)( 9,21)(10,22)(11,13)(12,14)(15,37)(16,38)
(17,35)(18,36)(23,24)(27,32)(28,31)(29,34)(30,33)(39,40);
s1 := Sym(42)!( 3,11)( 4,12)( 5,14)( 6,13)( 7,40)( 8,39)( 9,41)(10,42)(15,34)
(16,33)(17,32)(18,31)(19,25)(20,26)(21,23)(22,24)(27,28)(29,30);
s2 := Sym(42)!( 1, 2)( 3,25)( 4,26)( 5,24)( 6,23)( 7,16)( 8,15)( 9,17)(10,18)
(19,37)(20,38)(21,35)(22,36)(27,33)(28,34)(29,31)(30,32)(39,40)(41,42);
poly := sub<Sym(42)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*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