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# Polytope of Type {3,2,12,4}

Atlas Canonical Name : {3,2,12,4}*576b
if this polytope has a name.
Group : SmallGroup(576,8312)
Rank : 5
Schlafli Type : {3,2,12,4}
Number of vertices, edges, etc : 3, 3, 12, 24, 4
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{3,2,12,4,2} of size 1152
Vertex Figure Of :
{2,3,2,12,4} of size 1152
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {3,2,6,4}*288c
4-fold quotients : {3,2,3,4}*144
Covers (Minimal Covers in Boldface) :
2-fold covers : {3,2,24,4}*1152c, {3,2,24,4}*1152d, {3,2,12,4}*1152b, {6,2,12,4}*1152b
3-fold covers : {9,2,12,4}*1728b, {3,2,36,4}*1728b, {3,6,12,4}*1728b, {3,6,12,4}*1728e
Permutation Representation (GAP) :
```s0 := (2,3);;
s1 := (1,2);;
s2 := ( 5, 6)( 7, 8)( 9,19)(11,15)(12,14)(13,27)(16,32)(17,35)(18,20)(21,37)
(22,23)(24,40)(25,43)(26,33)(28,31)(29,47)(30,44)(34,46)(38,49)(39,41)(42,51)
(45,48);;
s3 := ( 4,11)( 5, 7)( 6,22)( 8,12)( 9,46)(10,14)(13,37)(15,23)(16,51)(17,45)
(18,29)(19,28)(20,32)(21,26)(24,47)(25,36)(27,41)(30,50)(31,42)(33,40)(34,39)
(35,44)(38,48)(43,49);;
s4 := ( 4,36)( 5,45)( 6,48)( 7,37)( 8,21)( 9,19)(10,50)(11,46)(12,29)(13,32)
(14,47)(15,34)(16,27)(17,20)(18,35)(22,51)(23,42)(24,40)(25,28)(26,44)(30,33)
(31,43)(38,41)(39,49);;
poly := Group([s0,s1,s2,s3,s4]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4,
s4*s3*s2*s4*s3*s4*s3*s2*s3, 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(51)!(2,3);
s1 := Sym(51)!(1,2);
s2 := Sym(51)!( 5, 6)( 7, 8)( 9,19)(11,15)(12,14)(13,27)(16,32)(17,35)(18,20)
(21,37)(22,23)(24,40)(25,43)(26,33)(28,31)(29,47)(30,44)(34,46)(38,49)(39,41)
(42,51)(45,48);
s3 := Sym(51)!( 4,11)( 5, 7)( 6,22)( 8,12)( 9,46)(10,14)(13,37)(15,23)(16,51)
(17,45)(18,29)(19,28)(20,32)(21,26)(24,47)(25,36)(27,41)(30,50)(31,42)(33,40)
(34,39)(35,44)(38,48)(43,49);
s4 := Sym(51)!( 4,36)( 5,45)( 6,48)( 7,37)( 8,21)( 9,19)(10,50)(11,46)(12,29)
(13,32)(14,47)(15,34)(16,27)(17,20)(18,35)(22,51)(23,42)(24,40)(25,28)(26,44)
(30,33)(31,43)(38,41)(39,49);
poly := sub<Sym(51)|s0,s1,s2,s3,s4>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1,
s3*s4*s3*s4*s3*s4*s3*s4, s4*s3*s2*s4*s3*s4*s3*s2*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

```

to this polytope