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# Polytope of Type {2,2,12,6}

Atlas Canonical Name : {2,2,12,6}*576c
if this polytope has a name.
Group : SmallGroup(576,8589)
Rank : 5
Schlafli Type : {2,2,12,6}
Number of vertices, edges, etc : 2, 2, 12, 36, 6
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,2,12,6,2} of size 1152
Vertex Figure Of :
{2,2,2,12,6} of size 1152
{3,2,2,12,6} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,2,6,6}*288b
3-fold quotients : {2,2,4,6}*192a
4-fold quotients : {2,2,6,3}*144
6-fold quotients : {2,2,2,6}*96
9-fold quotients : {2,2,4,2}*64
12-fold quotients : {2,2,2,3}*48
18-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,4,12,6}*1152c, {2,2,12,12}*1152b, {4,2,12,6}*1152a, {2,2,24,6}*1152a
3-fold covers : {2,2,12,18}*1728b, {2,2,12,6}*1728c, {2,2,12,6}*1728g, {2,6,12,6}*1728g, {6,2,12,6}*1728c
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(23,32)(24,34)(25,33)(26,35)
(27,37)(28,36)(29,38)(30,40)(31,39)(42,43)(45,46)(48,49)(51,52)(54,55)(57,58)
(59,68)(60,70)(61,69)(62,71)(63,73)(64,72)(65,74)(66,76)(67,75);;
s3 := ( 5,60)( 6,59)( 7,61)( 8,66)( 9,65)(10,67)(11,63)(12,62)(13,64)(14,69)
(15,68)(16,70)(17,75)(18,74)(19,76)(20,72)(21,71)(22,73)(23,42)(24,41)(25,43)
(26,48)(27,47)(28,49)(29,45)(30,44)(31,46)(32,51)(33,50)(34,52)(35,57)(36,56)
(37,58)(38,54)(39,53)(40,55);;
s4 := ( 5,44)( 6,46)( 7,45)( 8,41)( 9,43)(10,42)(11,47)(12,49)(13,48)(14,53)
(15,55)(16,54)(17,50)(18,52)(19,51)(20,56)(21,58)(22,57)(23,62)(24,64)(25,63)
(26,59)(27,61)(28,60)(29,65)(30,67)(31,66)(32,71)(33,73)(34,72)(35,68)(36,70)
(37,69)(38,74)(39,76)(40,75);;
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*s1*s0*s1,
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, s4*s2*s3*s2*s3*s4*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(76)!(1,2);
s1 := Sym(76)!(3,4);
s2 := Sym(76)!( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(23,32)(24,34)(25,33)
(26,35)(27,37)(28,36)(29,38)(30,40)(31,39)(42,43)(45,46)(48,49)(51,52)(54,55)
(57,58)(59,68)(60,70)(61,69)(62,71)(63,73)(64,72)(65,74)(66,76)(67,75);
s3 := Sym(76)!( 5,60)( 6,59)( 7,61)( 8,66)( 9,65)(10,67)(11,63)(12,62)(13,64)
(14,69)(15,68)(16,70)(17,75)(18,74)(19,76)(20,72)(21,71)(22,73)(23,42)(24,41)
(25,43)(26,48)(27,47)(28,49)(29,45)(30,44)(31,46)(32,51)(33,50)(34,52)(35,57)
(36,56)(37,58)(38,54)(39,53)(40,55);
s4 := Sym(76)!( 5,44)( 6,46)( 7,45)( 8,41)( 9,43)(10,42)(11,47)(12,49)(13,48)
(14,53)(15,55)(16,54)(17,50)(18,52)(19,51)(20,56)(21,58)(22,57)(23,62)(24,64)
(25,63)(26,59)(27,61)(28,60)(29,65)(30,67)(31,66)(32,71)(33,73)(34,72)(35,68)
(36,70)(37,69)(38,74)(39,76)(40,75);
poly := sub<Sym(76)|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*s1*s0*s1, 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,
s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

```

to this polytope