Polytope of Type {4,4,6}

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

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

Permutation Representation (Magma) :

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

References : None.
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