Polytope of Type {6,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6,4}*768e
if this polytope has a name.
Group : SmallGroup(768,1089286)
Rank : 4
Schlafli Type : {6,6,4}
Number of vertices, edges, etc : 16, 48, 32, 4
Order of s₀s₁s₂s₃ : 8
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 : {6,6,4}*384, {6,6,2}*384b
   4-fold quotients : {3,6,4}*192, {6,6,2}*192
   8-fold quotients : {3,6,2}*96, {6,3,2}*96
   16-fold quotients : {3,3,2}*48
   24-fold quotients : {2,2,4}*32
   48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
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