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# Polytope of Type {2,2,4,6}

Atlas Canonical Name : {2,2,4,6}*576
if this polytope has a name.
Group : SmallGroup(576,8666)
Rank : 5
Schlafli Type : {2,2,4,6}
Number of vertices, edges, etc : 2, 2, 12, 36, 18
Order of s0s1s2s3s4 : 4
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,2,4,6,2} of size 1152
{2,2,4,6,3} of size 1728
Vertex Figure Of :
{2,2,2,4,6} of size 1152
{3,2,2,4,6} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,2,4,6}*288
9-fold quotients : {2,2,4,2}*64
18-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,2,4,12}*1152, {2,4,4,6}*1152, {4,2,4,6}*1152, {2,2,8,6}*1152
3-fold covers : {2,2,4,6}*1728a, {2,2,12,6}*1728e, {2,2,12,6}*1728f, {2,2,4,6}*1728b, {2,2,12,6}*1728h, {2,6,4,6}*1728a, {6,2,4,6}*1728, {2,2,12,6}*1728i
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := (3,4);;
s2 := ( 8,11)( 9,12)(10,13)(17,20)(18,21)(19,22)(26,29)(27,30)(28,31)(35,38)
(36,39)(37,40)(41,50)(42,51)(43,52)(44,56)(45,57)(46,58)(47,53)(48,54)(49,55)
(59,68)(60,69)(61,70)(62,74)(63,75)(64,76)(65,71)(66,72)(67,73);;
s3 := ( 5,41)( 6,44)( 7,47)( 8,42)( 9,45)(10,48)(11,43)(12,46)(13,49)(14,50)
(15,53)(16,56)(17,51)(18,54)(19,57)(20,52)(21,55)(22,58)(23,59)(24,62)(25,65)
(26,60)(27,63)(28,66)(29,61)(30,64)(31,67)(32,68)(33,71)(34,74)(35,69)(36,72)
(37,75)(38,70)(39,73)(40,76);;
s4 := ( 5,33)( 6,32)( 7,34)( 8,39)( 9,38)(10,40)(11,36)(12,35)(13,37)(14,24)
(15,23)(16,25)(17,30)(18,29)(19,31)(20,27)(21,26)(22,28)(41,69)(42,68)(43,70)
(44,75)(45,74)(46,76)(47,72)(48,71)(49,73)(50,60)(51,59)(52,61)(53,66)(54,65)
(55,67)(56,63)(57,62)(58,64);;
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, s2*s3*s2*s3*s2*s3*s2*s3,
s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*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)!( 8,11)( 9,12)(10,13)(17,20)(18,21)(19,22)(26,29)(27,30)(28,31)
(35,38)(36,39)(37,40)(41,50)(42,51)(43,52)(44,56)(45,57)(46,58)(47,53)(48,54)
(49,55)(59,68)(60,69)(61,70)(62,74)(63,75)(64,76)(65,71)(66,72)(67,73);
s3 := Sym(76)!( 5,41)( 6,44)( 7,47)( 8,42)( 9,45)(10,48)(11,43)(12,46)(13,49)
(14,50)(15,53)(16,56)(17,51)(18,54)(19,57)(20,52)(21,55)(22,58)(23,59)(24,62)
(25,65)(26,60)(27,63)(28,66)(29,61)(30,64)(31,67)(32,68)(33,71)(34,74)(35,69)
(36,72)(37,75)(38,70)(39,73)(40,76);
s4 := Sym(76)!( 5,33)( 6,32)( 7,34)( 8,39)( 9,38)(10,40)(11,36)(12,35)(13,37)
(14,24)(15,23)(16,25)(17,30)(18,29)(19,31)(20,27)(21,26)(22,28)(41,69)(42,68)
(43,70)(44,75)(45,74)(46,76)(47,72)(48,71)(49,73)(50,60)(51,59)(52,61)(53,66)
(54,65)(55,67)(56,63)(57,62)(58,64);
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,
s2*s3*s2*s3*s2*s3*s2*s3, s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

```

to this polytope