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# Polytope of Type {2,12,8}

Atlas Canonical Name : {2,12,8}*768b
if this polytope has a name.
Group : SmallGroup(768,323571)
Rank : 4
Schlafli Type : {2,12,8}
Number of vertices, edges, etc : 2, 24, 96, 16
Order of s0s1s2s3 : 12
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}*384a
3-fold quotients : {2,4,8}*256b
4-fold quotients : {2,12,4}*192a
6-fold quotients : {2,4,4}*128
8-fold quotients : {2,12,2}*96, {2,6,4}*96a
12-fold quotients : {2,4,4}*64
16-fold quotients : {2,6,2}*48
24-fold quotients : {2,2,4}*32, {2,4,2}*32
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)( 4,53)( 5,52)( 6,54)( 7,56)( 8,55)( 9,57)(10,59)(11,58)(12,60)
(13,62)(14,61)(15,72)(16,74)(17,73)(18,69)(19,71)(20,70)(21,66)(22,68)(23,67)
(24,63)(25,65)(26,64)(27,75)(28,77)(29,76)(30,78)(31,80)(32,79)(33,81)(34,83)
(35,82)(36,84)(37,86)(38,85)(39,96)(40,98)(41,97)(42,93)(43,95)(44,94)(45,90)
(46,92)(47,91)(48,87)(49,89)(50,88);;
s2 := ( 3, 4)( 6, 7)( 9,13)(10,12)(11,14)(15,16)(18,19)(21,25)(22,24)(23,26)
(27,40)(28,39)(29,41)(30,43)(31,42)(32,44)(33,49)(34,48)(35,50)(36,46)(37,45)
(38,47)(51,52)(54,55)(57,61)(58,60)(59,62)(63,64)(66,67)(69,73)(70,72)(71,74)
(75,88)(76,87)(77,89)(78,91)(79,90)(80,92)(81,97)(82,96)(83,98)(84,94)(85,93)
(86,95);;
s3 := ( 3,75)( 4,76)( 5,77)( 6,78)( 7,79)( 8,80)( 9,81)(10,82)(11,83)(12,84)
(13,85)(14,86)(15,96)(16,97)(17,98)(18,93)(19,94)(20,95)(21,90)(22,91)(23,92)
(24,87)(25,88)(26,89)(27,51)(28,52)(29,53)(30,54)(31,55)(32,56)(33,57)(34,58)
(35,59)(36,60)(37,61)(38,62)(39,72)(40,73)(41,74)(42,69)(43,70)(44,71)(45,66)
(46,67)(47,68)(48,63)(49,64)(50,65);;
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*s1*s2*s3*s1*s2*s3*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

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

```

to this polytope