Polytope of Type {3,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,6,4}*384b
if this polytope has a name.
Group : SmallGroup(384,17948)
Rank : 4
Schlafli Type : {3,6,4}
Number of vertices, edges, etc : 4, 24, 32, 8
Order of s₀s₁s₂s₃ : 4
Order of s₀s₁s₂s₃s₂s₁ : 4
Special Properties :
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,6,4,2} of size 768
Vertex Figure Of :
   {2,3,6,4} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,3,4}*192
   4-fold quotients : {3,6,2}*96
   8-fold quotients : {3,3,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,12,4}*768a, {3,12,4}*768b, {3,6,4}*768a, {3,6,4}*768c, {6,6,4}*768a, {3,6,4}*768d, {3,12,4}*768c, {3,12,4}*768d, {6,6,4}*768d
   3-fold covers : {3,6,4}*1152a, {3,6,12}*1152
   5-fold covers : {3,6,20}*1920, {15,6,4}*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 := ( 1,17)( 2,20)( 3,19)( 4,18)( 5,21)( 6,24)( 7,23)( 8,22)( 9,29)(10,32)
(11,31)(12,30)(13,25)(14,28)(15,27)(16,26)(34,36)(38,40)(41,45)(42,48)(43,47)
(44,46)(49,65)(50,68)(51,67)(52,66)(53,69)(54,72)(55,71)(56,70)(57,77)(58,80)
(59,79)(60,78)(61,73)(62,76)(63,75)(64,74)(82,84)(86,88)(89,93)(90,96)(91,95)
(92,94);;
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, s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s3*s0*s2*s1*s3*s0*s2*s1*s3*s2*s0*s1*s3*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)!( 1,17)( 2,20)( 3,19)( 4,18)( 5,21)( 6,24)( 7,23)( 8,22)( 9,29)
(10,32)(11,31)(12,30)(13,25)(14,28)(15,27)(16,26)(34,36)(38,40)(41,45)(42,48)
(43,47)(44,46)(49,65)(50,68)(51,67)(52,66)(53,69)(54,72)(55,71)(56,70)(57,77)
(58,80)(59,79)(60,78)(61,73)(62,76)(63,75)(64,74)(82,84)(86,88)(89,93)(90,96)
(91,95)(92,94);
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, 
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s3*s0*s2*s1*s3*s0*s2*s1*s3*s2*s0*s1*s3*s2*s0*s1 >;

References : None.
to this polytope