Polytope of Type {3,4,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,4,8}*384
Also Known As : {{3,4},{4,8|2}}. if this polytope has another name.
Group : SmallGroup(384,18032)
Rank : 4
Schlafli Type : {3,4,8}
Number of vertices, edges, etc : 6, 12, 32, 8
Order of s₀s₁s₂s₃ : 24
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,4,8,2} of size 768
Vertex Figure Of :
   {2,3,4,8} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,4,4}*192b
   4-fold quotients : {3,2,8}*96, {3,4,2}*96
   8-fold quotients : {3,2,4}*48, {3,4,2}*48
   16-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,8,8}*768, {3,4,16}*768, {6,4,8}*768c
   3-fold covers : {9,4,8}*1152, {3,4,24}*1152, {3,12,8}*1152
   5-fold covers : {3,4,40}*1920, {15,4,8}*1920
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
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