Polytope of Type {2,4,4,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,4,6}*768c
if this polytope has a name.
Group : SmallGroup(768,1089108)
Rank : 5
Schlafli Type : {2,4,4,6}
Number of vertices, edges, etc : 2, 8, 16, 24, 6
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-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 : {2,4,4,3}*384a
4-fold quotients : {2,2,4,6}*192b
8-fold quotients : {2,2,4,3}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 7, 9)( 8,10)(11,14)(12,13)(15,16)(17,18)(23,25)(24,26)(27,30)(28,29)
(31,32)(33,34)(39,41)(40,42)(43,46)(44,45)(47,48)(49,50)(55,57)(56,58)(59,62)
(60,61)(63,64)(65,66)(71,73)(72,74)(75,78)(76,77)(79,80)(81,82)(87,89)(88,90)
(91,94)(92,93)(95,96)(97,98);;
s2 := ( 3,59)( 4,60)( 5,61)( 6,62)( 7,63)( 8,64)( 9,65)(10,66)(11,51)(12,52)
(13,53)(14,54)(15,55)(16,56)(17,57)(18,58)(19,75)(20,76)(21,77)(22,78)(23,79)
(24,80)(25,81)(26,82)(27,67)(28,68)(29,69)(30,70)(31,71)(32,72)(33,73)(34,74)
(35,91)(36,92)(37,93)(38,94)(39,95)(40,96)(41,97)(42,98)(43,83)(44,84)(45,85)
(46,86)(47,87)(48,88)(49,89)(50,90);;
s3 := ( 5, 6)( 7,11)( 8,12)( 9,14)(10,13)(17,18)(19,35)(20,36)(21,38)(22,37)
(23,43)(24,44)(25,46)(26,45)(27,39)(28,40)(29,42)(30,41)(31,47)(32,48)(33,50)
(34,49)(53,54)(55,59)(56,60)(57,62)(58,61)(65,66)(67,83)(68,84)(69,86)(70,85)
(71,91)(72,92)(73,94)(74,93)(75,87)(76,88)(77,90)(78,89)(79,95)(80,96)(81,98)
(82,97);;
s4 := ( 3,83)( 4,85)( 5,84)( 6,86)( 7,95)( 8,97)( 9,96)(10,98)(11,91)(12,93)
(13,92)(14,94)(15,87)(16,89)(17,88)(18,90)(19,67)(20,69)(21,68)(22,70)(23,79)
(24,81)(25,80)(26,82)(27,75)(28,77)(29,76)(30,78)(31,71)(32,73)(33,72)(34,74)
(35,51)(36,53)(37,52)(38,54)(39,63)(40,65)(41,64)(42,66)(43,59)(44,61)(45,60)
(46,62)(47,55)(48,57)(49,56)(50,58);;
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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s2*s3*s4*s2*s3*s4, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(98)!(1,2);
s1 := Sym(98)!( 7, 9)( 8,10)(11,14)(12,13)(15,16)(17,18)(23,25)(24,26)(27,30)
(28,29)(31,32)(33,34)(39,41)(40,42)(43,46)(44,45)(47,48)(49,50)(55,57)(56,58)
(59,62)(60,61)(63,64)(65,66)(71,73)(72,74)(75,78)(76,77)(79,80)(81,82)(87,89)
(88,90)(91,94)(92,93)(95,96)(97,98);
s2 := Sym(98)!( 3,59)( 4,60)( 5,61)( 6,62)( 7,63)( 8,64)( 9,65)(10,66)(11,51)
(12,52)(13,53)(14,54)(15,55)(16,56)(17,57)(18,58)(19,75)(20,76)(21,77)(22,78)
(23,79)(24,80)(25,81)(26,82)(27,67)(28,68)(29,69)(30,70)(31,71)(32,72)(33,73)
(34,74)(35,91)(36,92)(37,93)(38,94)(39,95)(40,96)(41,97)(42,98)(43,83)(44,84)
(45,85)(46,86)(47,87)(48,88)(49,89)(50,90);
s3 := Sym(98)!( 5, 6)( 7,11)( 8,12)( 9,14)(10,13)(17,18)(19,35)(20,36)(21,38)
(22,37)(23,43)(24,44)(25,46)(26,45)(27,39)(28,40)(29,42)(30,41)(31,47)(32,48)
(33,50)(34,49)(53,54)(55,59)(56,60)(57,62)(58,61)(65,66)(67,83)(68,84)(69,86)
(70,85)(71,91)(72,92)(73,94)(74,93)(75,87)(76,88)(77,90)(78,89)(79,95)(80,96)
(81,98)(82,97);
s4 := Sym(98)!( 3,83)( 4,85)( 5,84)( 6,86)( 7,95)( 8,97)( 9,96)(10,98)(11,91)
(12,93)(13,92)(14,94)(15,87)(16,89)(17,88)(18,90)(19,67)(20,69)(21,68)(22,70)
(23,79)(24,81)(25,80)(26,82)(27,75)(28,77)(29,76)(30,78)(31,71)(32,73)(33,72)
(34,74)(35,51)(36,53)(37,52)(38,54)(39,63)(40,65)(41,64)(42,66)(43,59)(44,61)
(45,60)(46,62)(47,55)(48,57)(49,56)(50,58);
poly := sub<Sym(98)|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*s1*s0*s1, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s2*s3*s4*s2*s3*s4,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 >;
to this polytope