Polytope of Type {4,4,6,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,6,3}*768
Also Known As : {{4,4|2},{4,6|2},{6,3}4}. if this polytope has another name.
Group : SmallGroup(768,1088763)
Rank : 5
Schlafli Type : {4,4,6,3}
Number of vertices, edges, etc : 4, 8, 16, 12, 4
Order of s0s1s2s3s4 : 4
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 : {2,4,6,3}*384, {4,2,6,3}*384
4-fold quotients : {4,2,3,3}*192, {2,2,6,3}*192
8-fold quotients : {2,2,3,3}*96
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 := ( 1,49)( 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);;
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);;
s4 := ( 1, 2)( 5,10)( 6, 9)( 7,11)( 8,12)(13,14)(17,22)(18,21)(19,23)(20,24)
(25,26)(29,34)(30,33)(31,35)(32,36)(37,38)(41,46)(42,45)(43,47)(44,48)(49,50)
(53,58)(54,57)(55,59)(56,60)(61,62)(65,70)(66,69)(67,71)(68,72)(73,74)(77,82)
(78,81)(79,83)(80,84)(85,86)(89,94)(90,93)(91,95)(92,96);;
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, s3*s4*s3*s4*s3*s4,
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s4*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
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)!( 1,49)( 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);
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);
s4 := Sym(96)!( 1, 2)( 5,10)( 6, 9)( 7,11)( 8,12)(13,14)(17,22)(18,21)(19,23)
(20,24)(25,26)(29,34)(30,33)(31,35)(32,36)(37,38)(41,46)(42,45)(43,47)(44,48)
(49,50)(53,58)(54,57)(55,59)(56,60)(61,62)(65,70)(66,69)(67,71)(68,72)(73,74)
(77,82)(78,81)(79,83)(80,84)(85,86)(89,94)(90,93)(91,95)(92,96);
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, s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s4*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope