Polytope of Type {3,4,4,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,4,4,4}*768b
Also Known As : {{3,4},{4,4|2},{4,4|2}}. if this polytope has another name.
Group : SmallGroup(768,1088763)
Rank : 5
Schlafli Type : {3,4,4,4}
Number of vertices, edges, etc : 6, 12, 16, 8, 4
Order of s₀s₁s₂s₃s₄ : 12
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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 : {3,4,2,4}*384, {3,4,4,2}*384b
   4-fold quotients : {3,2,4,4}*192, {3,4,2,4}*192, {3,4,2,2}*192
   8-fold quotients : {3,2,2,4}*96, {3,2,4,2}*96, {3,4,2,2}*96
   16-fold quotients : {3,2,2,2}*48
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)(49,57)
(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);;
s2 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)
(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)
(43,44)(45,46)(47,48)(49,62)(50,61)(51,64)(52,63)(53,66)(54,65)(55,68)(56,67)
(57,70)(58,69)(59,72)(60,71)(73,86)(74,85)(75,88)(76,87)(77,90)(78,89)(79,92)
(80,91)(81,94)(82,93)(83,96)(84,95);;
s3 := ( 1,49)( 2,50)( 3,51)( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,57)(10,58)
(11,59)(12,60)(13,61)(14,62)(15,63)(16,64)(17,65)(18,66)(19,67)(20,68)(21,69)
(22,70)(23,71)(24,72)(25,73)(26,74)(27,75)(28,76)(29,77)(30,78)(31,79)(32,80)
(33,81)(34,82)(35,83)(36,84)(37,85)(38,86)(39,87)(40,88)(41,89)(42,90)(43,91)
(44,92)(45,93)(46,94)(47,95)(48,96);;
s4 := (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,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4 ];;
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)
(49,57)(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);
s2 := Sym(96)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)
(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)
(41,42)(43,44)(45,46)(47,48)(49,62)(50,61)(51,64)(52,63)(53,66)(54,65)(55,68)
(56,67)(57,70)(58,69)(59,72)(60,71)(73,86)(74,85)(75,88)(76,87)(77,90)(78,89)
(79,92)(80,91)(81,94)(82,93)(83,96)(84,95);
s3 := Sym(96)!( 1,49)( 2,50)( 3,51)( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,57)
(10,58)(11,59)(12,60)(13,61)(14,62)(15,63)(16,64)(17,65)(18,66)(19,67)(20,68)
(21,69)(22,70)(23,71)(24,72)(25,73)(26,74)(27,75)(28,76)(29,77)(30,78)(31,79)
(32,80)(33,81)(34,82)(35,83)(36,84)(37,85)(38,86)(39,87)(40,88)(41,89)(42,90)
(43,91)(44,92)(45,93)(46,94)(47,95)(48,96);
s4 := 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,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4 >;

References : None.
to this polytope