Polytope of Type {2,4,6,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,6,8}*768b
if this polytope has a name.
Group : SmallGroup(768,1089270)
Rank : 5
Schlafli Type : {2,4,6,8}
Number of vertices, edges, etc : 2, 4, 12, 24, 8
Order of s0s1s2s3s4 : 24
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 : {2,4,6,4}*384c
4-fold quotients : {2,4,6,2}*192c
8-fold quotients : {2,4,3,2}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3, 5)( 4, 6)( 7, 9)( 8,10)(11,13)(12,14)(15,17)(16,18)(19,21)(20,22)
(23,25)(24,26)(27,29)(28,30)(31,33)(32,34)(35,37)(36,38)(39,41)(40,42)(43,45)
(44,46)(47,49)(48,50)(51,53)(52,54)(55,57)(56,58)(59,61)(60,62)(63,65)(64,66)
(67,69)(68,70)(71,73)(72,74)(75,77)(76,78)(79,81)(80,82)(83,85)(84,86)(87,89)
(88,90)(91,93)(92,94)(95,97)(96,98);;
s2 := ( 4, 5)( 7,11)( 8,13)( 9,12)(10,14)(16,17)(19,23)(20,25)(21,24)(22,26)
(28,29)(31,35)(32,37)(33,36)(34,38)(40,41)(43,47)(44,49)(45,48)(46,50)(52,53)
(55,59)(56,61)(57,60)(58,62)(64,65)(67,71)(68,73)(69,72)(70,74)(76,77)(79,83)
(80,85)(81,84)(82,86)(88,89)(91,95)(92,97)(93,96)(94,98);;
s3 := ( 3,11)( 4,14)( 5,13)( 6,12)( 8,10)(15,23)(16,26)(17,25)(18,24)(20,22)
(27,47)(28,50)(29,49)(30,48)(31,43)(32,46)(33,45)(34,44)(35,39)(36,42)(37,41)
(38,40)(51,83)(52,86)(53,85)(54,84)(55,79)(56,82)(57,81)(58,80)(59,75)(60,78)
(61,77)(62,76)(63,95)(64,98)(65,97)(66,96)(67,91)(68,94)(69,93)(70,92)(71,87)
(72,90)(73,89)(74,88);;
s4 := ( 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)(27,87)(28,88)(29,89)(30,90)(31,91)(32,92)(33,93)(34,94)
(35,95)(36,96)(37,97)(38,98)(39,75)(40,76)(41,77)(42,78)(43,79)(44,80)(45,81)
(46,82)(47,83)(48,84)(49,85)(50,86);;
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*s4*s3*s2*s3*s4*s3,
s1*s2*s3*s2*s1*s2*s3*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(98)!(1,2);
s1 := Sym(98)!( 3, 5)( 4, 6)( 7, 9)( 8,10)(11,13)(12,14)(15,17)(16,18)(19,21)
(20,22)(23,25)(24,26)(27,29)(28,30)(31,33)(32,34)(35,37)(36,38)(39,41)(40,42)
(43,45)(44,46)(47,49)(48,50)(51,53)(52,54)(55,57)(56,58)(59,61)(60,62)(63,65)
(64,66)(67,69)(68,70)(71,73)(72,74)(75,77)(76,78)(79,81)(80,82)(83,85)(84,86)
(87,89)(88,90)(91,93)(92,94)(95,97)(96,98);
s2 := Sym(98)!( 4, 5)( 7,11)( 8,13)( 9,12)(10,14)(16,17)(19,23)(20,25)(21,24)
(22,26)(28,29)(31,35)(32,37)(33,36)(34,38)(40,41)(43,47)(44,49)(45,48)(46,50)
(52,53)(55,59)(56,61)(57,60)(58,62)(64,65)(67,71)(68,73)(69,72)(70,74)(76,77)
(79,83)(80,85)(81,84)(82,86)(88,89)(91,95)(92,97)(93,96)(94,98);
s3 := Sym(98)!( 3,11)( 4,14)( 5,13)( 6,12)( 8,10)(15,23)(16,26)(17,25)(18,24)
(20,22)(27,47)(28,50)(29,49)(30,48)(31,43)(32,46)(33,45)(34,44)(35,39)(36,42)
(37,41)(38,40)(51,83)(52,86)(53,85)(54,84)(55,79)(56,82)(57,81)(58,80)(59,75)
(60,78)(61,77)(62,76)(63,95)(64,98)(65,97)(66,96)(67,91)(68,94)(69,93)(70,92)
(71,87)(72,90)(73,89)(74,88);
s4 := Sym(98)!( 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)(27,87)(28,88)(29,89)(30,90)(31,91)(32,92)(33,93)
(34,94)(35,95)(36,96)(37,97)(38,98)(39,75)(40,76)(41,77)(42,78)(43,79)(44,80)
(45,81)(46,82)(47,83)(48,84)(49,85)(50,86);
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*s4*s3*s2*s3*s4*s3, s1*s2*s3*s2*s1*s2*s3*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope