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

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

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

```

to this polytope