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# Polytope of Type {4,24,4}

Atlas Canonical Name : {4,24,4}*768c
if this polytope has a name.
Group : SmallGroup(768,201204)
Rank : 4
Schlafli Type : {4,24,4}
Number of vertices, edges, etc : 4, 48, 48, 4
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,12,4}*384a, {4,24,2}*384b
3-fold quotients : {4,8,4}*256c
4-fold quotients : {2,12,4}*192a, {4,12,2}*192a, {4,6,4}*192a
6-fold quotients : {4,4,4}*128, {4,8,2}*128b
8-fold quotients : {2,12,2}*96, {2,6,4}*96a, {4,6,2}*96a
12-fold quotients : {2,4,4}*64, {4,4,2}*64, {4,2,4}*64
16-fold quotients : {2,6,2}*48
24-fold quotients : {2,2,4}*32, {2,4,2}*32, {4,2,2}*32
32-fold quotients : {2,3,2}*24
48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (13,16)(14,17)(15,18)(19,22)(20,23)(21,24)(37,40)(38,41)(39,42)(43,46)
(44,47)(45,48);;
s1 := ( 2, 3)( 5, 6)( 8, 9)(11,12)(13,16)(14,18)(15,17)(19,22)(20,24)(21,23)
(25,37)(26,39)(27,38)(28,40)(29,42)(30,41)(31,43)(32,45)(33,44)(34,46)(35,48)
(36,47);;
s2 := ( 1,27)( 2,26)( 3,25)( 4,30)( 5,29)( 6,28)( 7,33)( 8,32)( 9,31)(10,36)
(11,35)(12,34)(13,42)(14,41)(15,40)(16,39)(17,38)(18,37)(19,48)(20,47)(21,46)
(22,45)(23,44)(24,43);;
s3 := (25,31)(26,32)(27,33)(28,34)(29,35)(30,36)(37,43)(38,44)(39,45)(40,46)
(41,47)(42,48);;
poly := Group([s0,s1,s2,s3]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1,
s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(48)!(13,16)(14,17)(15,18)(19,22)(20,23)(21,24)(37,40)(38,41)(39,42)
(43,46)(44,47)(45,48);
s1 := Sym(48)!( 2, 3)( 5, 6)( 8, 9)(11,12)(13,16)(14,18)(15,17)(19,22)(20,24)
(21,23)(25,37)(26,39)(27,38)(28,40)(29,42)(30,41)(31,43)(32,45)(33,44)(34,46)
(35,48)(36,47);
s2 := Sym(48)!( 1,27)( 2,26)( 3,25)( 4,30)( 5,29)( 6,28)( 7,33)( 8,32)( 9,31)
(10,36)(11,35)(12,34)(13,42)(14,41)(15,40)(16,39)(17,38)(18,37)(19,48)(20,47)
(21,46)(22,45)(23,44)(24,43);
s3 := Sym(48)!(25,31)(26,32)(27,33)(28,34)(29,35)(30,36)(37,43)(38,44)(39,45)
(40,46)(41,47)(42,48);
poly := sub<Sym(48)|s0,s1,s2,s3>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1,
s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1 >;

```
References : None.
to this polytope