# Polytope of Type {5,20}

Atlas Canonical Name : {5,20}*480
if this polytope has a name.
Group : SmallGroup(480,959)
Rank : 3
Schlafli Type : {5,20}
Number of vertices, edges, etc : 12, 120, 48
Order of s0s1s2 : 12
Order of s0s1s2s1 : 12
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{5,20,2} of size 960
{5,20,4} of size 1920
Vertex Figure Of :
{2,5,20} of size 960
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {5,10}*240
4-fold quotients : {5,5}*120, {5,10}*120a, {5,10}*120b
8-fold quotients : {5,5}*60
Covers (Minimal Covers in Boldface) :
2-fold covers : {10,20}*960b
3-fold covers : {15,20}*1440a
4-fold covers : {10,20}*1920, {20,20}*1920c, {20,20}*1920d
Permutation Representation (GAP) :
```s0 := ( 2,10)( 3,12)( 4,17)( 5,19)( 7,38)(11,28)(13,44)(14,43)(15,34)(20,23)
(21,36)(22,37)(24,26)(29,33)(30,31)(32,35)(39,47)(40,46)(41,45)(42,48);;
s1 := ( 2, 3)( 4,17)( 5,19)( 7,28)( 8,35)( 9,29)(10,15)(11,26)(12,39)(13,25)
(14,27)(20,38)(21,33)(22,44)(23,31)(24,30)(32,42)(34,41)(40,43)(45,47);;
s2 := ( 1, 8)( 2, 4)( 3,33)( 5,24)( 6,25)( 7,21)( 9,16)(10,17)(11,32)(12,29)
(13,31)(14,34)(15,43)(18,27)(19,26)(20,46)(22,39)(23,40)(28,35)(30,44)(36,38)
(37,47)(41,42)(45,48);;
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,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(48)!( 2,10)( 3,12)( 4,17)( 5,19)( 7,38)(11,28)(13,44)(14,43)(15,34)
(20,23)(21,36)(22,37)(24,26)(29,33)(30,31)(32,35)(39,47)(40,46)(41,45)(42,48);
s1 := Sym(48)!( 2, 3)( 4,17)( 5,19)( 7,28)( 8,35)( 9,29)(10,15)(11,26)(12,39)
(13,25)(14,27)(20,38)(21,33)(22,44)(23,31)(24,30)(32,42)(34,41)(40,43)(45,47);
s2 := Sym(48)!( 1, 8)( 2, 4)( 3,33)( 5,24)( 6,25)( 7,21)( 9,16)(10,17)(11,32)
(12,29)(13,31)(14,34)(15,43)(18,27)(19,26)(20,46)(22,39)(23,40)(28,35)(30,44)
(36,38)(37,47)(41,42)(45,48);
poly := sub<Sym(48)|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,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1 >;

```
References : None.
to this polytope