# Polytope of Type {24,3}

Atlas Canonical Name : {24,3}*576
if this polytope has a name.
Group : SmallGroup(576,5053)
Rank : 3
Schlafli Type : {24,3}
Number of vertices, edges, etc : 96, 144, 12
Order of s0s1s2 : 6
Order of s0s1s2s1 : 24
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{24,3,2} of size 1152
Vertex Figure Of :
{2,24,3} of size 1152
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {8,3}*192
4-fold quotients : {12,3}*144
12-fold quotients : {4,3}*48
16-fold quotients : {6,3}*36
24-fold quotients : {4,3}*24
48-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
2-fold covers : {24,3}*1152a, {24,6}*1152a, {24,6}*1152c
3-fold covers : {24,9}*1728, {24,3}*1728
Permutation Representation (GAP) :
```s0 := ( 1, 9)( 2,10)( 3,11)( 4,12)( 5,16)( 6,15)( 7,14)( 8,13)(17,41)(18,42)
(19,43)(20,44)(21,48)(22,47)(23,46)(24,45)(25,33)(26,34)(27,35)(28,36)(29,40)
(30,39)(31,38)(32,37);;
s1 := ( 1,17)( 2,18)( 3,20)( 4,19)( 5,28)( 6,27)( 7,25)( 8,26)( 9,23)(10,24)
(11,22)(12,21)(13,30)(14,29)(15,31)(16,32)(35,36)(37,44)(38,43)(39,41)(40,42)
(45,46);;
s2 := ( 2, 4)( 5,14)( 6,15)( 7,16)( 8,13)(10,12)(17,33)(18,36)(19,35)(20,34)
(21,46)(22,47)(23,48)(24,45)(25,41)(26,44)(27,43)(28,42)(29,40)(30,37)(31,38)
(32,39);;
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, s1*s2*s1*s2*s1*s2,
s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1,
s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope