Polytope of Type {6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4}*384b
if this polytope has a name.
Group : SmallGroup(384,18046)
Rank : 3
Schlafli Type : {6,4}
Number of vertices, edges, etc : 48, 96, 32
Order of s₀s₁s₂ : 24
Order of s₀s₁s₂s₁ : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {6,4,2} of size 768
Vertex Figure Of :
   {2,6,4} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,4}*192b
   4-fold quotients : {6,4}*96
   8-fold quotients : {6,4}*48a, {3,4}*48, {6,4}*48b, {6,4}*48c
   16-fold quotients : {3,4}*24, {6,2}*24
   24-fold quotients : {2,4}*16
   32-fold quotients : {3,2}*12
   48-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,8}*768j, {12,4}*768e
   3-fold covers : {18,4}*1152b, {6,12}*1152d, {6,12}*1152f
   5-fold covers : {6,20}*1920b, {30,4}*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)( 3,53)( 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*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*s0*s1*s0*s2*s1*s2*s1*s0*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)( 3,53)( 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*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*s0*s1*s0*s2*s1*s2*s1*s0*s1 >;

References : None.
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