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# Polytope of Type {24,4}

Atlas Canonical Name : {24,4}*384f
if this polytope has a name.
Group : SmallGroup(384,18046)
Rank : 3
Schlafli Type : {24,4}
Number of vertices, edges, etc : 48, 96, 8
Order of s0s1s2 : 6
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
{24,4,2} of size 768
Vertex Figure Of :
{2,24,4} of size 768
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {12,4}*192c
4-fold quotients : {6,4}*96
8-fold quotients : {3,4}*48, {6,4}*48b, {6,4}*48c
16-fold quotients : {3,4}*24, {6,2}*24
32-fold quotients : {3,2}*12
48-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {24,8}*768m, {24,8}*768p, {24,4}*768k
3-fold covers : {72,4}*1152f, {24,12}*1152s, {24,12}*1152x
5-fold covers : {24,20}*1920f, {120,4}*1920f
Permutation Representation (GAP) :
```s0 := ( 1,49)( 2,50)( 3,54)( 4,53)( 5,52)( 6,51)( 7,56)( 8,55)( 9,65)(10,66)
(11,70)(12,69)(13,68)(14,67)(15,72)(16,71)(17,57)(18,58)(19,62)(20,61)(21,60)
(22,59)(23,64)(24,63)(25,74)(26,73)(27,77)(28,78)(29,75)(30,76)(31,79)(32,80)
(33,90)(34,89)(35,93)(36,94)(37,91)(38,92)(39,95)(40,96)(41,82)(42,81)(43,85)
(44,86)(45,83)(46,84)(47,87)(48,88);;
s1 := ( 1, 9)( 2,10)( 3,12)( 4,11)( 5,15)( 6,16)( 7,13)( 8,14)(19,20)(21,23)
(22,24)(25,34)(26,33)(27,35)(28,36)(29,40)(30,39)(31,38)(32,37)(41,42)(45,48)
(46,47)(49,82)(50,81)(51,83)(52,84)(53,88)(54,87)(55,86)(56,85)(57,74)(58,73)
(59,75)(60,76)(61,80)(62,79)(63,78)(64,77)(65,90)(66,89)(67,91)(68,92)(69,96)
(70,95)(71,94)(72,93);;
s2 := ( 1,55)( 2,56)( 3,53)( 4,54)( 5,52)( 6,51)( 7,50)( 8,49)( 9,63)(10,64)
(11,61)(12,62)(13,60)(14,59)(15,58)(16,57)(17,71)(18,72)(19,69)(20,70)(21,68)
(22,67)(23,66)(24,65)(25,80)(26,79)(27,78)(28,77)(29,75)(30,76)(31,73)(32,74)
(33,88)(34,87)(35,86)(36,85)(37,83)(38,84)(39,81)(40,82)(41,96)(42,95)(43,94)
(44,93)(45,91)(46,92)(47,89)(48,90);;
poly := Group([s0,s1,s2]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s2*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

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

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s2*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;

```
References : None.
to this polytope