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# Polytope of Type {4,24}

Atlas Canonical Name : {4,24}*960a
if this polytope has a name.
Group : SmallGroup(960,5719)
Rank : 3
Schlafli Type : {4,24}
Number of vertices, edges, etc : 20, 240, 120
Order of s0s1s2 : 20
Order of s0s1s2s1 : 3
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,24,2} of size 1920
Vertex Figure Of :
{2,4,24} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,12}*480b
4-fold quotients : {4,6}*240b
8-fold quotients : {4,6}*120
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,24}*1920c
Permutation Representation (GAP) :
```s0 := ( 1,12)( 2,10)( 3,15)( 4,37)( 5,44)( 6,20)( 7,17)( 8,48)( 9,29)(11,21)
(13,28)(14,40)(16,41)(18,46)(19,32)(22,26)(23,25)(24,31)(27,39)(30,45)(33,38)
(34,47)(35,36)(42,43);;
s1 := ( 1, 3)( 2,21)( 4,48)( 5,32)( 6, 9)( 7,40)( 8,14)(10,36)(11,25)(12,20)
(13,39)(15,29)(16,31)(17,37)(18,38)(19,33)(22,47)(23,35)(24,43)(26,34)(27,28)
(30,42)(41,45)(44,46);;
s2 := ( 1,12)( 2,16)( 3,40)( 4,24)( 5,39)( 6,30)( 7,22)( 8,48)( 9,47)(10,41)
(11,21)(13,35)(14,15)(17,26)(18,23)(19,42)(20,45)(25,46)(27,44)(28,36)(29,34)
(31,37)(32,43)(33,38);;
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*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope