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# Polytope of Type {6,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,24}*384a
if this polytope has a name.
Group : SmallGroup(384,18032)
Rank : 3
Schlafli Type : {6,24}
Number of vertices, edges, etc : 8, 96, 32
Order of s0s1s2 : 8
Order of s0s1s2s1 : 6
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{6,24,2} of size 768
Vertex Figure Of :
{2,6,24} of size 768
{3,6,24} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {6,12}*192a
4-fold quotients : {6,6}*96
8-fold quotients : {3,6}*48, {6,3}*48
12-fold quotients : {2,8}*32
16-fold quotients : {3,3}*24
24-fold quotients : {2,4}*16
48-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {6,24}*768, {12,24}*768a, {12,24}*768c, {6,48}*768a, {6,48}*768b
3-fold covers : {6,24}*1152g, {6,24}*1152j
5-fold covers : {6,120}*1920a, {30,24}*1920a
Permutation Representation (GAP) :
```s0 := ( 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);;
s1 := ( 1, 5)( 2, 6)( 3, 8)( 4, 7)(11,12)(13,17)(14,18)(15,20)(16,19)(23,24)
(25,41)(26,42)(27,44)(28,43)(29,37)(30,38)(31,40)(32,39)(33,45)(34,46)(35,48)
(36,47)(49,77)(50,78)(51,80)(52,79)(53,73)(54,74)(55,76)(56,75)(57,81)(58,82)
(59,84)(60,83)(61,89)(62,90)(63,92)(64,91)(65,85)(66,86)(67,88)(68,87)(69,93)
(70,94)(71,96)(72,95);;
s2 := ( 1,52)( 2,50)( 3,51)( 4,49)( 5,60)( 6,58)( 7,59)( 8,57)( 9,56)(10,54)
(11,55)(12,53)(13,64)(14,62)(15,63)(16,61)(17,72)(18,70)(19,71)(20,69)(21,68)
(22,66)(23,67)(24,65)(25,88)(26,86)(27,87)(28,85)(29,96)(30,94)(31,95)(32,93)
(33,92)(34,90)(35,91)(36,89)(37,76)(38,74)(39,75)(40,73)(41,84)(42,82)(43,83)
(44,81)(45,80)(46,78)(47,79)(48,77);;
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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope