Polytope of Type {24,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,6}*384b
if this polytope has a name.
Group : SmallGroup(384,18046)
Rank : 3
Schlafli Type : {24,6}
Number of vertices, edges, etc : 32, 96, 8
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 :
   {24,6,2} of size 768
Vertex Figure Of :
   {2,24,6} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,6}*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 : {4,2}*16
   48-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {24,6}*768, {24,12}*768b, {24,12}*768d
   3-fold covers : {24,6}*1152i, {24,6}*1152m
   5-fold covers : {120,6}*1920b, {24,30}*1920b
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, 7)( 2, 8)( 5, 6)( 9,23)(10,24)(11,19)(12,20)(13,22)(14,21)(15,17)
(16,18)(25,31)(26,32)(29,30)(33,47)(34,48)(35,43)(36,44)(37,46)(38,45)(39,41)
(40,42)(49,56)(50,55)(51,52)(57,72)(58,71)(59,68)(60,67)(61,69)(62,70)(63,66)
(64,65)(73,80)(74,79)(75,76)(81,96)(82,95)(83,92)(84,91)(85,93)(86,94)(87,90)
(88,89);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s2*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*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, 7)( 2, 8)( 5, 6)( 9,23)(10,24)(11,19)(12,20)(13,22)(14,21)
(15,17)(16,18)(25,31)(26,32)(29,30)(33,47)(34,48)(35,43)(36,44)(37,46)(38,45)
(39,41)(40,42)(49,56)(50,55)(51,52)(57,72)(58,71)(59,68)(60,67)(61,69)(62,70)
(63,66)(64,65)(73,80)(74,79)(75,76)(81,96)(82,95)(83,92)(84,91)(85,93)(86,94)
(87,90)(88,89);
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s2*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1 >;

References : None.
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