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# Polytope of Type {2,12,8}

Atlas Canonical Name : {2,12,8}*768g
if this polytope has a name.
Group : SmallGroup(768,1089251)
Rank : 4
Schlafli Type : {2,12,8}
Number of vertices, edges, etc : 2, 24, 96, 16
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,12,4}*384c, {2,6,8}*384c
4-fold quotients : {2,6,4}*192
8-fold quotients : {2,3,4}*96, {2,6,4}*96b, {2,6,4}*96c
16-fold quotients : {2,3,4}*48, {2,6,2}*48
32-fold quotients : {2,3,2}*24
48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 3,51)( 4,52)( 5,56)( 6,55)( 7,54)( 8,53)( 9,58)(10,57)(11,67)(12,68)
(13,72)(14,71)(15,70)(16,69)(17,74)(18,73)(19,59)(20,60)(21,64)(22,63)(23,62)
(24,61)(25,66)(26,65)(27,75)(28,76)(29,80)(30,79)(31,78)(32,77)(33,82)(34,81)
(35,91)(36,92)(37,96)(38,95)(39,94)(40,93)(41,98)(42,97)(43,83)(44,84)(45,88)
(46,87)(47,86)(48,85)(49,90)(50,89);;
s2 := ( 3,11)( 4,12)( 5,14)( 6,13)( 7,17)( 8,18)( 9,15)(10,16)(21,22)(23,25)
(24,26)(27,35)(28,36)(29,38)(30,37)(31,41)(32,42)(33,39)(34,40)(45,46)(47,49)
(48,50)(51,84)(52,83)(53,85)(54,86)(55,90)(56,89)(57,88)(58,87)(59,76)(60,75)
(61,77)(62,78)(63,82)(64,81)(65,80)(66,79)(67,92)(68,91)(69,93)(70,94)(71,98)
(72,97)(73,96)(74,95);;
s3 := ( 3,57)( 4,58)( 5,55)( 6,56)( 7,54)( 8,53)( 9,52)(10,51)(11,65)(12,66)
(13,63)(14,64)(15,62)(16,61)(17,60)(18,59)(19,73)(20,74)(21,71)(22,72)(23,70)
(24,69)(25,68)(26,67)(27,81)(28,82)(29,79)(30,80)(31,78)(32,77)(33,76)(34,75)
(35,89)(36,90)(37,87)(38,88)(39,86)(40,85)(41,84)(42,83)(43,97)(44,98)(45,95)
(46,96)(47,94)(48,93)(49,92)(50,91);;
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*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s1*s2*s1*s3*s2*s3*s2*s3*s2*s1*s2*s1*s2*s1*s2,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 ];;
poly := F / rels;;

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

```

to this polytope