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# Polytope of Type {6,4,2}

Atlas Canonical Name : {6,4,2}*288
if this polytope has a name.
Group : SmallGroup(288,1031)
Rank : 4
Schlafli Type : {6,4,2}
Number of vertices, edges, etc : 18, 36, 12, 2
Order of s0s1s2s3 : 4
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{6,4,2,2} of size 576
{6,4,2,3} of size 864
{6,4,2,4} of size 1152
{6,4,2,5} of size 1440
{6,4,2,6} of size 1728
Vertex Figure Of :
{2,6,4,2} of size 576
{3,6,4,2} of size 864
{4,6,4,2} of size 1152
{6,6,4,2} of size 1728
{6,6,4,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {6,4,2}*144
9-fold quotients : {2,4,2}*32
18-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {6,8,2}*576, {6,4,4}*576, {12,4,2}*576
3-fold covers : {6,4,2}*864a, {6,12,2}*864e, {6,12,2}*864f, {6,4,6}*864b, {6,4,2}*864b, {6,12,2}*864h, {6,12,2}*864i
4-fold covers : {12,4,4}*1152, {6,4,8}*1152a, {24,4,2}*1152a, {12,8,2}*1152a, {6,8,4}*1152a, {24,4,2}*1152b, {6,4,8}*1152b, {12,8,2}*1152b, {6,8,4}*1152b, {12,4,2}*1152, {6,4,4}*1152a, {6,16,2}*1152
5-fold covers : {6,4,10}*1440c, {30,4,2}*1440, {6,20,2}*1440
6-fold covers : {6,8,2}*1728a, {6,24,2}*1728d, {6,24,2}*1728e, {6,4,4}*1728a, {6,12,4}*1728h, {6,12,4}*1728i, {12,4,2}*1728b, {12,12,2}*1728f, {12,12,2}*1728g, {6,8,6}*1728a, {6,4,12}*1728a, {12,4,2}*1728d, {12,12,2}*1728j, {6,8,2}*1728b, {6,24,2}*1728g, {6,4,4}*1728c, {6,12,4}*1728o, {12,4,6}*1728b, {6,24,2}*1728h, {6,12,4}*1728q, {12,12,2}*1728l
Permutation Representation (GAP) :
```s0 := ( 1,28)( 2,30)( 3,29)( 4,34)( 5,36)( 6,35)( 7,31)( 8,33)( 9,32)(10,19)
(11,21)(12,20)(13,25)(14,27)(15,26)(16,22)(17,24)(18,23)(37,64)(38,66)(39,65)
(40,70)(41,72)(42,71)(43,67)(44,69)(45,68)(46,55)(47,57)(48,56)(49,61)(50,63)
(51,62)(52,58)(53,60)(54,59);;
s1 := ( 1, 4)( 2, 5)( 3, 6)(10,13)(11,14)(12,15)(19,22)(20,23)(21,24)(28,31)
(29,32)(30,33)(37,49)(38,50)(39,51)(40,46)(41,47)(42,48)(43,52)(44,53)(45,54)
(55,67)(56,68)(57,69)(58,64)(59,65)(60,66)(61,70)(62,71)(63,72);;
s2 := ( 1,37)( 2,40)( 3,43)( 4,38)( 5,41)( 6,44)( 7,39)( 8,42)( 9,45)(10,46)
(11,49)(12,52)(13,47)(14,50)(15,53)(16,48)(17,51)(18,54)(19,55)(20,58)(21,61)
(22,56)(23,59)(24,62)(25,57)(26,60)(27,63)(28,64)(29,67)(30,70)(31,65)(32,68)
(33,71)(34,66)(35,69)(36,72);;
s3 := (73,74);;
poly := Group([s0,s1,s2,s3]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

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

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

```

to this polytope