Polytope of Type {6,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,24}*384b
if this polytope has a name.
Group : SmallGroup(384,18046)
Rank : 3
Schlafli Type : {6,24}
Number of vertices, edges, etc : 8, 96, 32
Order of s₀s₁s₂ : 4
Order of s₀s₁s₂s₁ : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {6,24,2} of size 768
Vertex Figure Of :
   {2,6,24} of size 768
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
   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}*768b, {12,24}*768d
   3-fold covers : {6,24}*1152i, {6,24}*1152m
   5-fold covers : {6,120}*1920b, {30,24}*1920b
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
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