Polytope of Type {2,4,12,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,12,3}*768
if this polytope has a name.
Group : SmallGroup(768,1089251)
Rank : 5
Schlafli Type : {2,4,12,3}
Number of vertices, edges, etc : 2, 4, 32, 24, 4
Order of s0s1s2s3s4 : 8
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 : {2,4,6,3}*384, {2,2,12,3}*384
4-fold quotients : {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 := (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 := ( 3,51)( 4,52)( 5,56)( 6,55)( 7,54)( 8,53)( 9,58)(10,57)(11,67)(12,68)
(13,72)(14,71)(15,70)(16,69)(17,74)(18,73)(19,59)(20,60)(21,64)(22,63)(23,62)
(24,61)(25,66)(26,65)(27,75)(28,76)(29,80)(30,79)(31,78)(32,77)(33,82)(34,81)
(35,91)(36,92)(37,96)(38,95)(39,94)(40,93)(41,98)(42,97)(43,83)(44,84)(45,88)
(46,87)(47,86)(48,85)(49,90)(50,89);;
s3 := ( 3,11)( 4,12)( 5,14)( 6,13)( 7,17)( 8,18)( 9,15)(10,16)(21,22)(23,25)
(24,26)(27,35)(28,36)(29,38)(30,37)(31,41)(32,42)(33,39)(34,40)(45,46)(47,49)
(48,50)(51,60)(52,59)(53,61)(54,62)(55,66)(56,65)(57,64)(58,63)(67,68)(71,74)
(72,73)(75,84)(76,83)(77,85)(78,86)(79,90)(80,89)(81,88)(82,87)(91,92)(95,98)
(96,97);;
s4 := ( 3,10)( 4, 9)( 5, 6)(11,26)(12,25)(13,22)(14,21)(15,23)(16,24)(17,20)
(18,19)(27,34)(28,33)(29,30)(35,50)(36,49)(37,46)(38,45)(39,47)(40,48)(41,44)
(42,43)(51,57)(52,58)(55,56)(59,73)(60,74)(61,69)(62,70)(63,72)(64,71)(65,67)
(66,68)(75,81)(76,82)(79,80)(83,97)(84,98)(85,93)(86,94)(87,96)(88,95)(89,91)
(90,92);;
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, s4*s2*s3*s2*s3*s2*s3*s4*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)!( 3,51)( 4,52)( 5,56)( 6,55)( 7,54)( 8,53)( 9,58)(10,57)(11,67)
(12,68)(13,72)(14,71)(15,70)(16,69)(17,74)(18,73)(19,59)(20,60)(21,64)(22,63)
(23,62)(24,61)(25,66)(26,65)(27,75)(28,76)(29,80)(30,79)(31,78)(32,77)(33,82)
(34,81)(35,91)(36,92)(37,96)(38,95)(39,94)(40,93)(41,98)(42,97)(43,83)(44,84)
(45,88)(46,87)(47,86)(48,85)(49,90)(50,89);
s3 := Sym(98)!( 3,11)( 4,12)( 5,14)( 6,13)( 7,17)( 8,18)( 9,15)(10,16)(21,22)
(23,25)(24,26)(27,35)(28,36)(29,38)(30,37)(31,41)(32,42)(33,39)(34,40)(45,46)
(47,49)(48,50)(51,60)(52,59)(53,61)(54,62)(55,66)(56,65)(57,64)(58,63)(67,68)
(71,74)(72,73)(75,84)(76,83)(77,85)(78,86)(79,90)(80,89)(81,88)(82,87)(91,92)
(95,98)(96,97);
s4 := Sym(98)!( 3,10)( 4, 9)( 5, 6)(11,26)(12,25)(13,22)(14,21)(15,23)(16,24)
(17,20)(18,19)(27,34)(28,33)(29,30)(35,50)(36,49)(37,46)(38,45)(39,47)(40,48)
(41,44)(42,43)(51,57)(52,58)(55,56)(59,73)(60,74)(61,69)(62,70)(63,72)(64,71)
(65,67)(66,68)(75,81)(76,82)(79,80)(83,97)(84,98)(85,93)(86,94)(87,96)(88,95)
(89,91)(90,92);
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,
s4*s2*s3*s2*s3*s2*s3*s4*s2*s3*s2*s3*s2*s3 >;
to this polytope