Polytope of Type {6,3,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,3,4}*384b
if this polytope has a name.
Group : SmallGroup(384,17948)
Rank : 4
Schlafli Type : {6,3,4}
Number of vertices, edges, etc : 8, 24, 16, 8
Order of s₀s₁s₂s₃ : 4
Order of s₀s₁s₂s₃s₂s₁ : 4
Special Properties :
   Locally Toroidal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,3,4,2} of size 768
Vertex Figure Of :
   {2,6,3,4} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,3,4}*192
   4-fold quotients : {6,3,2}*96
   8-fold quotients : {3,3,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,3,4}*768a, {6,3,4}*768, {6,6,4}*768c, {12,3,4}*768b, {6,6,4}*768d
   3-fold covers : {6,3,4}*1152a
   5-fold covers : {6,15,4}*1920
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope