Polytope of Type {2,3,4,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,4,8}*768
if this polytope has a name.
Group : SmallGroup(768,1089270)
Rank : 5
Schlafli Type : {2,3,4,8}
Number of vertices, edges, etc : 2, 6, 12, 32, 8
Order of s0s1s2s3s4 : 24
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
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 : {2,3,4,4}*384b
4-fold quotients : {2,3,2,8}*192, {2,3,4,2}*192
8-fold quotients : {2,3,2,4}*96, {2,3,4,2}*96
16-fold quotients : {2,3,2,2}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 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);;
s2 := ( 3, 7)( 4, 8)( 5,10)( 6, 9)(13,14)(15,19)(16,20)(17,22)(18,21)(25,26)
(27,31)(28,32)(29,34)(30,33)(37,38)(39,43)(40,44)(41,46)(42,45)(49,50)(51,55)
(52,56)(53,58)(54,57)(61,62)(63,67)(64,68)(65,70)(66,69)(73,74)(75,79)(76,80)
(77,82)(78,81)(85,86)(87,91)(88,92)(89,94)(90,93)(97,98);;
s3 := ( 3, 6)( 4, 5)( 7,10)( 8, 9)(11,14)(12,13)(15,18)(16,17)(19,22)(20,21)
(23,26)(24,25)(27,42)(28,41)(29,40)(30,39)(31,46)(32,45)(33,44)(34,43)(35,50)
(36,49)(37,48)(38,47)(51,78)(52,77)(53,76)(54,75)(55,82)(56,81)(57,80)(58,79)
(59,86)(60,85)(61,84)(62,83)(63,90)(64,89)(65,88)(66,87)(67,94)(68,93)(69,92)
(70,91)(71,98)(72,97)(73,96)(74,95);;
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, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s4*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)!( 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);
s2 := Sym(98)!( 3, 7)( 4, 8)( 5,10)( 6, 9)(13,14)(15,19)(16,20)(17,22)(18,21)
(25,26)(27,31)(28,32)(29,34)(30,33)(37,38)(39,43)(40,44)(41,46)(42,45)(49,50)
(51,55)(52,56)(53,58)(54,57)(61,62)(63,67)(64,68)(65,70)(66,69)(73,74)(75,79)
(76,80)(77,82)(78,81)(85,86)(87,91)(88,92)(89,94)(90,93)(97,98);
s3 := Sym(98)!( 3, 6)( 4, 5)( 7,10)( 8, 9)(11,14)(12,13)(15,18)(16,17)(19,22)
(20,21)(23,26)(24,25)(27,42)(28,41)(29,40)(30,39)(31,46)(32,45)(33,44)(34,43)
(35,50)(36,49)(37,48)(38,47)(51,78)(52,77)(53,76)(54,75)(55,82)(56,81)(57,80)
(58,79)(59,86)(60,85)(61,84)(62,83)(63,90)(64,89)(65,88)(66,87)(67,94)(68,93)
(69,92)(70,91)(71,98)(72,97)(73,96)(74,95);
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,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope