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

Atlas Canonical Name : {4,12,2,2}*384c
if this polytope has a name.
Group : SmallGroup(384,20049)
Rank : 5
Schlafli Type : {4,12,2,2}
Number of vertices, edges, etc : 4, 24, 12, 2, 2
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,12,2,2,2} of size 768
{4,12,2,2,3} of size 1152
{4,12,2,2,5} of size 1920
Vertex Figure Of :
{2,4,12,2,2} of size 768
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,6,2,2}*192c
4-fold quotients : {4,3,2,2}*96
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,12,4,2}*768e, {4,12,2,4}*768c, {4,12,2,2}*768b
3-fold covers : {4,36,2,2}*1152c, {4,12,2,6}*1152c, {4,12,6,2}*1152f, {4,12,6,2}*1152g
5-fold covers : {4,12,2,10}*1920c, {4,12,10,2}*1920c, {4,60,2,2}*1920c
Permutation Representation (GAP) :
```s0 := ( 1,21)( 2,13)( 3,10)( 4,35)( 5,36)( 6, 7)( 8,27)( 9,28)(11,22)(12,23)
(14,19)(15,20)(16,47)(17,48)(18,46)(24,42)(25,44)(26,40)(29,45)(30,43)(31,41)
(32,39)(33,37)(34,38);;
s1 := ( 2, 3)( 4, 5)( 6,16)( 8,12)( 9,11)(10,24)(13,29)(14,32)(15,17)(18,34)
(19,20)(21,37)(22,40)(23,30)(25,28)(26,44)(27,41)(31,43)(35,46)(36,38)(39,48)
(42,45);;
s2 := ( 1, 9)( 2, 5)( 3,20)( 4, 8)( 6,23)( 7,12)(10,15)(11,19)(13,36)(14,22)
(16,26)(17,43)(18,29)(21,28)(24,39)(25,34)(27,35)(30,48)(31,37)(32,42)(33,41)
(38,44)(40,47)(45,46);;
s3 := (49,50);;
s4 := (51,52);;
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,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(52)!( 1,21)( 2,13)( 3,10)( 4,35)( 5,36)( 6, 7)( 8,27)( 9,28)(11,22)
(12,23)(14,19)(15,20)(16,47)(17,48)(18,46)(24,42)(25,44)(26,40)(29,45)(30,43)
(31,41)(32,39)(33,37)(34,38);
s1 := Sym(52)!( 2, 3)( 4, 5)( 6,16)( 8,12)( 9,11)(10,24)(13,29)(14,32)(15,17)
(18,34)(19,20)(21,37)(22,40)(23,30)(25,28)(26,44)(27,41)(31,43)(35,46)(36,38)
(39,48)(42,45);
s2 := Sym(52)!( 1, 9)( 2, 5)( 3,20)( 4, 8)( 6,23)( 7,12)(10,15)(11,19)(13,36)
(14,22)(16,26)(17,43)(18,29)(21,28)(24,39)(25,34)(27,35)(30,48)(31,37)(32,42)
(33,41)(38,44)(40,47)(45,46);
s3 := Sym(52)!(49,50);
s4 := Sym(52)!(51,52);
poly := sub<Sym(52)|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, s0*s3*s0*s3,
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4,
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1 >;

```

to this polytope