Polytope of Type {8,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,6}*384f
if this polytope has a name.
Group : SmallGroup(384,17958)
Rank : 3
Schlafli Type : {8,6}
Number of vertices, edges, etc : 32, 96, 24
Order of s₀s₁s₂ : 12
Order of s₀s₁s₂s₁ : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {8,6,2} of size 768
Vertex Figure Of :
   {2,8,6} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,6}*192b, {8,6}*192b, {8,6}*192c
   4-fold quotients : {8,3}*96, {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, {8,12}*768p, {8,12}*768s
   3-fold covers : {8,18}*1152f, {24,6}*1152d, {24,6}*1152l
   5-fold covers : {40,6}*1920b, {8,30}*1920f
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)(25,77)(26,78)(27,80)(28,79)(29,74)(30,73)(31,75)(32,76)
(33,85)(34,86)(35,88)(36,87)(37,82)(38,81)(39,83)(40,84)(41,93)(42,94)(43,96)
(44,95)(45,90)(46,89)(47,91)(48,92);;
s1 := ( 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)(49,74)(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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0, 
s0*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*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)(25,77)(26,78)(27,80)(28,79)(29,74)(30,73)(31,75)
(32,76)(33,85)(34,86)(35,88)(36,87)(37,82)(38,81)(39,83)(40,84)(41,93)(42,94)
(43,96)(44,95)(45,90)(46,89)(47,91)(48,92);
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)(27,30)(28,29)(31,32)(33,41)(34,42)(35,46)(36,45)(37,44)(38,43)
(39,48)(40,47)(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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0, 
s0*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1 >;

References : None.
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