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# Polytope of Type {8,12,2}

Atlas Canonical Name : {8,12,2}*384a
if this polytope has a name.
Group : SmallGroup(384,11319)
Rank : 4
Schlafli Type : {8,12,2}
Number of vertices, edges, etc : 8, 48, 12, 2
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{8,12,2,2} of size 768
{8,12,2,3} of size 1152
{8,12,2,5} of size 1920
Vertex Figure Of :
{2,8,12,2} of size 768
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,12,2}*192a, {8,6,2}*192
3-fold quotients : {8,4,2}*128a
4-fold quotients : {2,12,2}*96, {4,6,2}*96a
6-fold quotients : {4,4,2}*64, {8,2,2}*64
8-fold quotients : {2,6,2}*48
12-fold quotients : {2,4,2}*32, {4,2,2}*32
16-fold quotients : {2,3,2}*24
24-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {8,12,2}*768a, {8,24,2}*768a, {8,24,2}*768c, {8,12,4}*768a, {16,12,2}*768a, {16,12,2}*768b
3-fold covers : {8,36,2}*1152a, {8,12,6}*1152a, {8,12,6}*1152b, {24,12,2}*1152a, {24,12,2}*1152c
5-fold covers : {8,60,2}*1920a, {8,12,10}*1920a, {40,12,2}*1920a
Permutation Representation (GAP) :
```s0 := ( 1,49)( 2,50)( 3,51)( 4,52)( 5,53)( 6,54)( 7,58)( 8,59)( 9,60)(10,55)
(11,56)(12,57)(13,61)(14,62)(15,63)(16,64)(17,65)(18,66)(19,70)(20,71)(21,72)
(22,67)(23,68)(24,69)(25,79)(26,80)(27,81)(28,82)(29,83)(30,84)(31,73)(32,74)
(33,75)(34,76)(35,77)(36,78)(37,91)(38,92)(39,93)(40,94)(41,95)(42,96)(43,85)
(44,86)(45,87)(46,88)(47,89)(48,90);;
s1 := ( 1,25)( 2,27)( 3,26)( 4,28)( 5,30)( 6,29)( 7,34)( 8,36)( 9,35)(10,31)
(11,33)(12,32)(13,37)(14,39)(15,38)(16,40)(17,42)(18,41)(19,46)(20,48)(21,47)
(22,43)(23,45)(24,44)(49,73)(50,75)(51,74)(52,76)(53,78)(54,77)(55,82)(56,84)
(57,83)(58,79)(59,81)(60,80)(61,85)(62,87)(63,86)(64,88)(65,90)(66,89)(67,94)
(68,96)(69,95)(70,91)(71,93)(72,92);;
s2 := ( 1, 2)( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,38)(26,37)
(27,39)(28,41)(29,40)(30,42)(31,44)(32,43)(33,45)(34,47)(35,46)(36,48)(49,50)
(52,53)(55,56)(58,59)(61,62)(64,65)(67,68)(70,71)(73,86)(74,85)(75,87)(76,89)
(77,88)(78,90)(79,92)(80,91)(81,93)(82,95)(83,94)(84,96);;
s3 := (97,98);;
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,
s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
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)!( 1,49)( 2,50)( 3,51)( 4,52)( 5,53)( 6,54)( 7,58)( 8,59)( 9,60)
(10,55)(11,56)(12,57)(13,61)(14,62)(15,63)(16,64)(17,65)(18,66)(19,70)(20,71)
(21,72)(22,67)(23,68)(24,69)(25,79)(26,80)(27,81)(28,82)(29,83)(30,84)(31,73)
(32,74)(33,75)(34,76)(35,77)(36,78)(37,91)(38,92)(39,93)(40,94)(41,95)(42,96)
(43,85)(44,86)(45,87)(46,88)(47,89)(48,90);
s1 := Sym(98)!( 1,25)( 2,27)( 3,26)( 4,28)( 5,30)( 6,29)( 7,34)( 8,36)( 9,35)
(10,31)(11,33)(12,32)(13,37)(14,39)(15,38)(16,40)(17,42)(18,41)(19,46)(20,48)
(21,47)(22,43)(23,45)(24,44)(49,73)(50,75)(51,74)(52,76)(53,78)(54,77)(55,82)
(56,84)(57,83)(58,79)(59,81)(60,80)(61,85)(62,87)(63,86)(64,88)(65,90)(66,89)
(67,94)(68,96)(69,95)(70,91)(71,93)(72,92);
s2 := Sym(98)!( 1, 2)( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,38)
(26,37)(27,39)(28,41)(29,40)(30,42)(31,44)(32,43)(33,45)(34,47)(35,46)(36,48)
(49,50)(52,53)(55,56)(58,59)(61,62)(64,65)(67,68)(70,71)(73,86)(74,85)(75,87)
(76,89)(77,88)(78,90)(79,92)(80,91)(81,93)(82,95)(83,94)(84,96);
s3 := Sym(98)!(97,98);
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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
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