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# Polytope of Type {8,4,3}

Atlas Canonical Name : {8,4,3}*384
Also Known As : {{8,4|2},{4,3}}. if this polytope has another name.
Group : SmallGroup(384,18032)
Rank : 4
Schlafli Type : {8,4,3}
Number of vertices, edges, etc : 8, 32, 12, 6
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{8,4,3,2} of size 768
Vertex Figure Of :
{2,8,4,3} of size 768
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,4,3}*192b
4-fold quotients : {8,2,3}*96, {2,4,3}*96
8-fold quotients : {4,2,3}*48, {2,4,3}*48
16-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
2-fold covers : {8,8,3}*768, {16,4,3}*768, {8,4,6}*768c
3-fold covers : {8,4,9}*1152, {24,4,3}*1152, {8,12,3}*1152
5-fold covers : {40,4,3}*1920, {8,4,15}*1920
Permutation Representation (GAP) :
```s0 := (25,37)(26,38)(27,39)(28,40)(29,41)(30,42)(31,43)(32,44)(33,45)(34,46)
(35,47)(36,48)(49,73)(50,74)(51,75)(52,76)(53,77)(54,78)(55,79)(56,80)(57,81)
(58,82)(59,83)(60,84)(61,85)(62,86)(63,87)(64,88)(65,89)(66,90)(67,91)(68,92)
(69,93)(70,94)(71,95)(72,96);;
s1 := ( 1,51)( 2,52)( 3,49)( 4,50)( 5,55)( 6,56)( 7,53)( 8,54)( 9,59)(10,60)
(11,57)(12,58)(13,63)(14,64)(15,61)(16,62)(17,67)(18,68)(19,65)(20,66)(21,71)
(22,72)(23,69)(24,70)(25,87)(26,88)(27,85)(28,86)(29,91)(30,92)(31,89)(32,90)
(33,95)(34,96)(35,93)(36,94)(37,75)(38,76)(39,73)(40,74)(41,79)(42,80)(43,77)
(44,78)(45,83)(46,84)(47,81)(48,82);;
s2 := ( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(17,21)(18,23)(19,22)(20,24)
(26,27)(29,33)(30,35)(31,34)(32,36)(38,39)(41,45)(42,47)(43,46)(44,48)(50,51)
(53,57)(54,59)(55,58)(56,60)(62,63)(65,69)(66,71)(67,70)(68,72)(74,75)(77,81)
(78,83)(79,82)(80,84)(86,87)(89,93)(90,95)(91,94)(92,96);;
s3 := ( 1, 9)( 2,12)( 3,11)( 4,10)( 6, 8)(13,21)(14,24)(15,23)(16,22)(18,20)
(25,33)(26,36)(27,35)(28,34)(30,32)(37,45)(38,48)(39,47)(40,46)(42,44)(49,57)
(50,60)(51,59)(52,58)(54,56)(61,69)(62,72)(63,71)(64,70)(66,68)(73,81)(74,84)
(75,83)(76,82)(78,80)(85,93)(86,96)(87,95)(88,94)(90,92);;
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*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope