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# Polytope of Type {4,8,12}

Atlas Canonical Name : {4,8,12}*768b
if this polytope has a name.
Group : SmallGroup(768,201202)
Rank : 4
Schlafli Type : {4,8,12}
Number of vertices, edges, etc : 4, 16, 48, 12
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 : {4,4,12}*384, {4,8,6}*384b
3-fold quotients : {4,8,4}*256c
4-fold quotients : {2,4,12}*192a, {4,2,12}*192, {4,4,6}*192
6-fold quotients : {4,4,4}*128, {4,8,2}*128b
8-fold quotients : {2,2,12}*96, {2,4,6}*96a, {4,2,6}*96
12-fold quotients : {2,4,4}*64, {4,4,2}*64, {4,2,4}*64
16-fold quotients : {4,2,3}*48, {2,2,6}*48
24-fold quotients : {2,2,4}*32, {2,4,2}*32, {4,2,2}*32
32-fold quotients : {2,2,3}*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 := (13,16)(14,17)(15,18)(19,22)(20,23)(21,24)(25,37)(26,38)(27,39)(28,40)
(29,41)(30,42)(31,43)(32,44)(33,45)(34,46)(35,47)(36,48);;
s2 := ( 1,25)( 2,27)( 3,26)( 4,28)( 5,30)( 6,29)( 7,31)( 8,33)( 9,32)(10,34)
(11,36)(12,35)(13,40)(14,42)(15,41)(16,37)(17,39)(18,38)(19,46)(20,48)(21,47)
(22,43)(23,45)(24,44);;
s3 := ( 1, 3)( 4, 6)( 7, 9)(10,12)(13,15)(16,18)(19,21)(22,24)(25,36)(26,35)
(27,34)(28,33)(29,32)(30,31)(37,48)(38,47)(39,46)(40,45)(41,44)(42,43);;
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*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
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)!(13,16)(14,17)(15,18)(19,22)(20,23)(21,24)(25,37)(26,38)(27,39)
(28,40)(29,41)(30,42)(31,43)(32,44)(33,45)(34,46)(35,47)(36,48);
s2 := Sym(48)!( 1,25)( 2,27)( 3,26)( 4,28)( 5,30)( 6,29)( 7,31)( 8,33)( 9,32)
(10,34)(11,36)(12,35)(13,40)(14,42)(15,41)(16,37)(17,39)(18,38)(19,46)(20,48)
(21,47)(22,43)(23,45)(24,44);
s3 := Sym(48)!( 1, 3)( 4, 6)( 7, 9)(10,12)(13,15)(16,18)(19,21)(22,24)(25,36)
(26,35)(27,34)(28,33)(29,32)(30,31)(37,48)(38,47)(39,46)(40,45)(41,44)(42,43);
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*s0*s1*s2*s1*s2*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

```
References : None.
to this polytope