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# Polytope of Type {2,6,8}

Atlas Canonical Name : {2,6,8}*384b
if this polytope has a name.
Group : SmallGroup(384,20062)
Rank : 4
Schlafli Type : {2,6,8}
Number of vertices, edges, etc : 2, 12, 48, 16
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,6,8,2} of size 768
Vertex Figure Of :
{2,2,6,8} of size 768
{3,2,6,8} of size 1152
{5,2,6,8} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,3,8}*192, {2,6,4}*192
4-fold quotients : {2,3,4}*96, {2,6,4}*96b, {2,6,4}*96c
8-fold quotients : {2,3,4}*48, {2,6,2}*48
16-fold quotients : {2,3,2}*24
24-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,12,8}*768e, {2,6,8}*768f, {2,12,8}*768h, {4,6,8}*768c
3-fold covers : {2,18,8}*1152b, {2,6,24}*1152b, {6,6,8}*1152b, {6,6,8}*1152c, {2,6,24}*1152e
5-fold covers : {10,6,8}*1920a, {2,6,40}*1920c, {2,30,8}*1920b
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 5, 7)( 6, 8)( 9,10)(11,19)(12,20)(13,23)(14,24)(15,21)(16,22)(17,26)
(18,25)(27,28)(29,32)(30,31)(35,44)(36,43)(37,48)(38,47)(39,46)(40,45)(41,49)
(42,50)(53,55)(54,56)(57,58)(59,67)(60,68)(61,71)(62,72)(63,69)(64,70)(65,74)
(66,73)(75,76)(77,80)(78,79)(83,92)(84,91)(85,96)(86,95)(87,94)(88,93)(89,97)
(90,98);;
s2 := ( 3,59)( 4,60)( 5,62)( 6,61)( 7,65)( 8,66)( 9,63)(10,64)(11,51)(12,52)
(13,54)(14,53)(15,57)(16,58)(17,55)(18,56)(19,67)(20,68)(21,70)(22,69)(23,73)
(24,74)(25,71)(26,72)(27,84)(28,83)(29,85)(30,86)(31,90)(32,89)(33,88)(34,87)
(35,76)(36,75)(37,77)(38,78)(39,82)(40,81)(41,80)(42,79)(43,92)(44,91)(45,93)
(46,94)(47,98)(48,97)(49,96)(50,95);;
s3 := ( 3,33)( 4,34)( 5,31)( 6,32)( 7,30)( 8,29)( 9,28)(10,27)(11,41)(12,42)
(13,39)(14,40)(15,38)(16,37)(17,36)(18,35)(19,49)(20,50)(21,47)(22,48)(23,46)
(24,45)(25,44)(26,43)(51,81)(52,82)(53,79)(54,80)(55,78)(56,77)(57,76)(58,75)
(59,89)(60,90)(61,87)(62,88)(63,86)(64,85)(65,84)(66,83)(67,97)(68,98)(69,95)
(70,96)(71,94)(72,93)(73,92)(74,91);;
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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(98)!(1,2);
s1 := Sym(98)!( 5, 7)( 6, 8)( 9,10)(11,19)(12,20)(13,23)(14,24)(15,21)(16,22)
(17,26)(18,25)(27,28)(29,32)(30,31)(35,44)(36,43)(37,48)(38,47)(39,46)(40,45)
(41,49)(42,50)(53,55)(54,56)(57,58)(59,67)(60,68)(61,71)(62,72)(63,69)(64,70)
(65,74)(66,73)(75,76)(77,80)(78,79)(83,92)(84,91)(85,96)(86,95)(87,94)(88,93)
(89,97)(90,98);
s2 := Sym(98)!( 3,59)( 4,60)( 5,62)( 6,61)( 7,65)( 8,66)( 9,63)(10,64)(11,51)
(12,52)(13,54)(14,53)(15,57)(16,58)(17,55)(18,56)(19,67)(20,68)(21,70)(22,69)
(23,73)(24,74)(25,71)(26,72)(27,84)(28,83)(29,85)(30,86)(31,90)(32,89)(33,88)
(34,87)(35,76)(36,75)(37,77)(38,78)(39,82)(40,81)(41,80)(42,79)(43,92)(44,91)
(45,93)(46,94)(47,98)(48,97)(49,96)(50,95);
s3 := Sym(98)!( 3,33)( 4,34)( 5,31)( 6,32)( 7,30)( 8,29)( 9,28)(10,27)(11,41)
(12,42)(13,39)(14,40)(15,38)(16,37)(17,36)(18,35)(19,49)(20,50)(21,47)(22,48)
(23,46)(24,45)(25,44)(26,43)(51,81)(52,82)(53,79)(54,80)(55,78)(56,77)(57,76)
(58,75)(59,89)(60,90)(61,87)(62,88)(63,86)(64,85)(65,84)(66,83)(67,97)(68,98)
(69,95)(70,96)(71,94)(72,93)(73,92)(74,91);
poly := sub<Sym(98)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2 >;

```

to this polytope