# Polytope of Type {6,10}

Atlas Canonical Name : {6,10}*480a
if this polytope has a name.
Group : SmallGroup(480,948)
Rank : 3
Schlafli Type : {6,10}
Number of vertices, edges, etc : 24, 120, 40
Order of s0s1s2 : 8
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{6,10,2} of size 960
Vertex Figure Of :
{2,6,10} of size 960
{4,6,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {6,5}*240a
4-fold quotients : {6,5}*120a
Covers (Minimal Covers in Boldface) :
2-fold covers : {6,10}*960a
3-fold covers : {6,30}*1440a, {6,30}*1440b
4-fold covers : {12,10}*1920b, {6,20}*1920c
Permutation Representation (GAP) :
```s0 := ( 1,11)( 2,24)( 3, 9)( 4,10)( 5,12)( 6,25)( 7,40)( 8,39)(13,19)(14,36)
(15,27)(16,28)(17,18)(20,22)(26,35)(29,38)(30,37)(31,32)(33,34);;
s1 := ( 3,10)( 4, 9)( 7,26)( 8,17)(11,22)(12,23)(13,16)(14,15)(18,37)(19,38)
(20,25)(21,24)(27,32)(28,31)(29,36)(30,35)(33,40)(34,39);;
s2 := ( 1,16)( 2, 8)( 3,33)( 4,32)( 5,15)( 6, 7)( 9,34)(10,31)(11,28)(12,27)
(13,19)(14,18)(17,36)(24,39)(25,40)(26,35)(29,37)(30,38);;
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,
s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(40)!( 1,11)( 2,24)( 3, 9)( 4,10)( 5,12)( 6,25)( 7,40)( 8,39)(13,19)
(14,36)(15,27)(16,28)(17,18)(20,22)(26,35)(29,38)(30,37)(31,32)(33,34);
s1 := Sym(40)!( 3,10)( 4, 9)( 7,26)( 8,17)(11,22)(12,23)(13,16)(14,15)(18,37)
(19,38)(20,25)(21,24)(27,32)(28,31)(29,36)(30,35)(33,40)(34,39);
s2 := Sym(40)!( 1,16)( 2, 8)( 3,33)( 4,32)( 5,15)( 6, 7)( 9,34)(10,31)(11,28)
(12,27)(13,19)(14,18)(17,36)(24,39)(25,40)(26,35)(29,37)(30,38);
poly := sub<Sym(40)|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,
s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1 >;

```
References : None.
to this polytope