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# Polytope of Type {6,24}

Atlas Canonical Name : {6,24}*576a
if this polytope has a name.
Group : SmallGroup(576,5053)
Rank : 3
Schlafli Type : {6,24}
Number of vertices, edges, etc : 12, 144, 48
Order of s0s1s2 : 3
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{6,24,2} of size 1152
Vertex Figure Of :
{2,6,24} of size 1152
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {6,8}*192a
4-fold quotients : {6,12}*144d
12-fold quotients : {6,4}*48b
24-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
2-fold covers : {12,24}*1152g, {12,24}*1152h, {6,24}*1152c
3-fold covers : {6,72}*1728a, {18,24}*1728a, {6,24}*1728a
Permutation Representation (GAP) :
```s0 := ( 3, 4)( 5,10)( 6, 9)( 7,11)( 8,12)(15,16)(19,20)(21,26)(22,25)(23,27)
(24,28)(31,32)(35,36)(37,42)(38,41)(39,43)(40,44)(47,48);;
s1 := ( 2, 3)( 5, 8)( 9,16)(10,14)(11,15)(12,13)(17,33)(18,35)(19,34)(20,36)
(21,40)(22,38)(23,39)(24,37)(25,48)(26,46)(27,47)(28,45)(29,44)(30,42)(31,43)
(32,41);;
s2 := ( 1,29)( 2,30)( 3,31)( 4,32)( 5,25)( 6,26)( 7,27)( 8,28)( 9,21)(10,22)
(11,23)(12,24)(13,17)(14,18)(15,19)(16,20)(33,45)(34,46)(35,47)(36,48)(37,41)
(38,42)(39,43)(40,44);;
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*s2*s0*s1*s2*s0*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope