Polytope of Type {2,4,8,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,8,3}*768
if this polytope has a name.
Group : SmallGroup(768,1089251)
Rank : 5
Schlafli Type : {2,4,8,3}
Number of vertices, edges, etc : 2, 4, 32, 24, 6
Order of s0s1s2s3s4 : 12
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 : {2,4,4,3}*384b, {2,2,8,3}*384
4-fold quotients : {2,2,4,3}*192
8-fold quotients : {2,4,2,3}*96, {2,2,4,3}*96
16-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (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)(73,97)(74,98);;
s2 := ( 3,55)( 4,56)( 5,58)( 6,57)( 7,52)( 8,51)( 9,53)(10,54)(11,63)(12,64)
(13,66)(14,65)(15,60)(16,59)(17,61)(18,62)(19,71)(20,72)(21,74)(22,73)(23,68)
(24,67)(25,69)(26,70)(27,79)(28,80)(29,82)(30,81)(31,76)(32,75)(33,77)(34,78)
(35,87)(36,88)(37,90)(38,89)(39,84)(40,83)(41,85)(42,86)(43,95)(44,96)(45,98)
(46,97)(47,92)(48,91)(49,93)(50,94);;
s3 := ( 5, 8)( 6, 7)( 9,10)(11,19)(12,20)(13,24)(14,23)(15,22)(16,21)(17,26)
(18,25)(29,32)(30,31)(33,34)(35,43)(36,44)(37,48)(38,47)(39,46)(40,45)(41,50)
(42,49)(51,52)(53,55)(54,56)(59,68)(60,67)(61,71)(62,72)(63,69)(64,70)(65,73)
(66,74)(75,76)(77,79)(78,80)(83,92)(84,91)(85,95)(86,96)(87,93)(88,94)(89,97)
(90,98);;
s4 := ( 3,19)( 4,20)( 5,25)( 6,26)( 7,24)( 8,23)( 9,21)(10,22)(13,17)(14,18)
(15,16)(27,43)(28,44)(29,49)(30,50)(31,48)(32,47)(33,45)(34,46)(37,41)(38,42)
(39,40)(51,68)(52,67)(53,74)(54,73)(55,71)(56,72)(57,70)(58,69)(59,60)(61,66)
(62,65)(75,92)(76,91)(77,98)(78,97)(79,95)(80,96)(81,94)(82,93)(83,84)(85,90)
(86,89);;
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,
s3*s4*s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s4*s3*s2*s4*s3*s2*s3*s2*s4*s3*s2*s4*s3*s2*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(98)!(1,2);
s1 := Sym(98)!(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)(73,97)(74,98);
s2 := Sym(98)!( 3,55)( 4,56)( 5,58)( 6,57)( 7,52)( 8,51)( 9,53)(10,54)(11,63)
(12,64)(13,66)(14,65)(15,60)(16,59)(17,61)(18,62)(19,71)(20,72)(21,74)(22,73)
(23,68)(24,67)(25,69)(26,70)(27,79)(28,80)(29,82)(30,81)(31,76)(32,75)(33,77)
(34,78)(35,87)(36,88)(37,90)(38,89)(39,84)(40,83)(41,85)(42,86)(43,95)(44,96)
(45,98)(46,97)(47,92)(48,91)(49,93)(50,94);
s3 := Sym(98)!( 5, 8)( 6, 7)( 9,10)(11,19)(12,20)(13,24)(14,23)(15,22)(16,21)
(17,26)(18,25)(29,32)(30,31)(33,34)(35,43)(36,44)(37,48)(38,47)(39,46)(40,45)
(41,50)(42,49)(51,52)(53,55)(54,56)(59,68)(60,67)(61,71)(62,72)(63,69)(64,70)
(65,73)(66,74)(75,76)(77,79)(78,80)(83,92)(84,91)(85,95)(86,96)(87,93)(88,94)
(89,97)(90,98);
s4 := Sym(98)!( 3,19)( 4,20)( 5,25)( 6,26)( 7,24)( 8,23)( 9,21)(10,22)(13,17)
(14,18)(15,16)(27,43)(28,44)(29,49)(30,50)(31,48)(32,47)(33,45)(34,46)(37,41)
(38,42)(39,40)(51,68)(52,67)(53,74)(54,73)(55,71)(56,72)(57,70)(58,69)(59,60)
(61,66)(62,65)(75,92)(76,91)(77,98)(78,97)(79,95)(80,96)(81,94)(82,93)(83,84)
(85,90)(86,89);
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, s3*s4*s3*s4*s3*s4,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s4*s3*s2*s4*s3*s2*s3*s2*s4*s3*s2*s4*s3*s2*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope