Polytope of Type {8,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,6,4}*384b
if this polytope has a name.
Group : SmallGroup(384,18032)
Rank : 4
Schlafli Type : {8,6,4}
Number of vertices, edges, etc : 8, 24, 12, 4
Order of s₀s₁s₂s₃ : 24
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {8,6,4,2} of size 768
Vertex Figure Of :
   {2,8,6,4} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,6,4}*192b
   4-fold quotients : {2,6,4}*96c
   8-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,12,4}*768c, {8,12,4}*768d, {16,6,4}*768b, {8,6,4}*768a
   3-fold covers : {8,18,4}*1152b, {24,6,4}*1152d, {24,6,4}*1152e
   5-fold covers : {40,6,4}*1920b, {8,30,4}*1920b
Permutation Representation (GAP) :

s0 := (25,37)(26,38)(27,39)(28,40)(29,41)(30,42)(31,43)(32,44)(33,45)(34,46)
(35,47)(36,48)(49,73)(50,74)(51,75)(52,76)(53,77)(54,78)(55,79)(56,80)(57,81)
(58,82)(59,83)(60,84)(61,85)(62,86)(63,87)(64,88)(65,89)(66,90)(67,91)(68,92)
(69,93)(70,94)(71,95)(72,96);;
s1 := ( 1,49)( 2,51)( 3,50)( 4,52)( 5,57)( 6,59)( 7,58)( 8,60)( 9,53)(10,55)
(11,54)(12,56)(13,61)(14,63)(15,62)(16,64)(17,69)(18,71)(19,70)(20,72)(21,65)
(22,67)(23,66)(24,68)(25,85)(26,87)(27,86)(28,88)(29,93)(30,95)(31,94)(32,96)
(33,89)(34,91)(35,90)(36,92)(37,73)(38,75)(39,74)(40,76)(41,81)(42,83)(43,82)
(44,84)(45,77)(46,79)(47,78)(48,80);;
s2 := ( 1, 5)( 2, 6)( 3, 8)( 4, 7)(11,12)(13,17)(14,18)(15,20)(16,19)(23,24)
(25,29)(26,30)(27,32)(28,31)(35,36)(37,41)(38,42)(39,44)(40,43)(47,48)(49,53)
(50,54)(51,56)(52,55)(59,60)(61,65)(62,66)(63,68)(64,67)(71,72)(73,77)(74,78)
(75,80)(76,79)(83,84)(85,89)(86,90)(87,92)(88,91)(95,96);;
s3 := ( 1, 4)( 2, 3)( 5, 8)( 6, 7)( 9,12)(10,11)(13,16)(14,15)(17,20)(18,19)
(21,24)(22,23)(25,28)(26,27)(29,32)(30,31)(33,36)(34,35)(37,40)(38,39)(41,44)
(42,43)(45,48)(46,47)(49,52)(50,51)(53,56)(54,55)(57,60)(58,59)(61,64)(62,63)
(65,68)(66,67)(69,72)(70,71)(73,76)(74,75)(77,80)(78,79)(81,84)(82,83)(85,88)
(86,87)(89,92)(90,91)(93,96)(94,95);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s3*s2*s3*s2*s3*s2*s3, s3*s2*s1*s3*s2*s3*s2*s1*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(96)!(25,37)(26,38)(27,39)(28,40)(29,41)(30,42)(31,43)(32,44)(33,45)
(34,46)(35,47)(36,48)(49,73)(50,74)(51,75)(52,76)(53,77)(54,78)(55,79)(56,80)
(57,81)(58,82)(59,83)(60,84)(61,85)(62,86)(63,87)(64,88)(65,89)(66,90)(67,91)
(68,92)(69,93)(70,94)(71,95)(72,96);
s1 := Sym(96)!( 1,49)( 2,51)( 3,50)( 4,52)( 5,57)( 6,59)( 7,58)( 8,60)( 9,53)
(10,55)(11,54)(12,56)(13,61)(14,63)(15,62)(16,64)(17,69)(18,71)(19,70)(20,72)
(21,65)(22,67)(23,66)(24,68)(25,85)(26,87)(27,86)(28,88)(29,93)(30,95)(31,94)
(32,96)(33,89)(34,91)(35,90)(36,92)(37,73)(38,75)(39,74)(40,76)(41,81)(42,83)
(43,82)(44,84)(45,77)(46,79)(47,78)(48,80);
s2 := Sym(96)!( 1, 5)( 2, 6)( 3, 8)( 4, 7)(11,12)(13,17)(14,18)(15,20)(16,19)
(23,24)(25,29)(26,30)(27,32)(28,31)(35,36)(37,41)(38,42)(39,44)(40,43)(47,48)
(49,53)(50,54)(51,56)(52,55)(59,60)(61,65)(62,66)(63,68)(64,67)(71,72)(73,77)
(74,78)(75,80)(76,79)(83,84)(85,89)(86,90)(87,92)(88,91)(95,96);
s3 := Sym(96)!( 1, 4)( 2, 3)( 5, 8)( 6, 7)( 9,12)(10,11)(13,16)(14,15)(17,20)
(18,19)(21,24)(22,23)(25,28)(26,27)(29,32)(30,31)(33,36)(34,35)(37,40)(38,39)
(41,44)(42,43)(45,48)(46,47)(49,52)(50,51)(53,56)(54,55)(57,60)(58,59)(61,64)
(62,63)(65,68)(66,67)(69,72)(70,71)(73,76)(74,75)(77,80)(78,79)(81,84)(82,83)
(85,88)(86,87)(89,92)(90,91)(93,96)(94,95);
poly := sub<Sym(96)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s2*s1*s3*s2*s3*s2*s1*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 >;

References : None.
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