Polytope of Type {6,4,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4,4}*768e
if this polytope has a name.
Group : SmallGroup(768,1088763)
Rank : 4
Schlafli Type : {6,4,4}
Number of vertices, edges, etc : 24, 48, 32, 4
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,4,4}*384d, {6,4,2}*384b
   4-fold quotients : {6,4,4}*192, {3,4,4}*192b, {6,4,2}*192
   8-fold quotients : {6,2,4}*96, {6,4,2}*96a, {3,4,2}*96, {6,4,2}*96b, {6,4,2}*96c
   12-fold quotients : {2,4,4}*64
   16-fold quotients : {3,2,4}*48, {3,4,2}*48, {6,2,2}*48
   24-fold quotients : {2,2,4}*32, {2,4,2}*32
   32-fold quotients : {3,2,2}*24
   48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
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