# Polytope of Type {10,20}

Atlas Canonical Name : {10,20}*960b
if this polytope has a name.
Group : SmallGroup(960,10889)
Rank : 3
Schlafli Type : {10,20}
Number of vertices, edges, etc : 24, 240, 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 :
{10,20,2} of size 1920
Vertex Figure Of :
{2,10,20} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {5,20}*480, {10,10}*480
4-fold quotients : {5,10}*240, {10,5}*240, {10,10}*240a, {10,10}*240b, {10,10}*240c, {10,10}*240d
8-fold quotients : {5,5}*120, {5,10}*120a, {5,10}*120b, {10,5}*120a, {10,5}*120b
16-fold quotients : {5,5}*60
120-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {10,20}*1920, {20,20}*1920c, {20,20}*1920d
Permutation Representation (GAP) :
```s0 := ( 2,45)( 3,41)( 4,17)( 5,19)( 7,30)( 8,48)( 9,36)(10,47)(11,23)(12,34)
(13,22)(14,40)(15,39)(20,26)(21,29)(24,38)(25,37)(27,46)(28,31)(35,42);;
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)
(49,50);;
s2 := ( 1,32)( 2,27)( 3,22)( 4,34)( 5,28)( 6,44)( 7,14)( 8,24)( 9,10)(11,21)
(12,17)(13,41)(15,42)(16,33)(18,43)(19,31)(20,37)(23,29)(25,26)(30,40)(35,39)
(36,47)(38,48)(45,46);;
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*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s0*s1*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*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(50)!( 2,45)( 3,41)( 4,17)( 5,19)( 7,30)( 8,48)( 9,36)(10,47)(11,23)
(12,34)(13,22)(14,40)(15,39)(20,26)(21,29)(24,38)(25,37)(27,46)(28,31)(35,42);
s1 := Sym(50)!( 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)
(49,50);
s2 := Sym(50)!( 1,32)( 2,27)( 3,22)( 4,34)( 5,28)( 6,44)( 7,14)( 8,24)( 9,10)
(11,21)(12,17)(13,41)(15,42)(16,33)(18,43)(19,31)(20,37)(23,29)(25,26)(30,40)
(35,39)(36,47)(38,48)(45,46);
poly := sub<Sym(50)|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*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s0*s1*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*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s0*s1 >;

```
References : None.
to this polytope