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

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

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

```

to this polytope