Polytope of Type {4,6}

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

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

Permutation Representation (Magma) :

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

References : None.
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