Polytope of Type {2,4,12,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,12,4}*768c
if this polytope has a name.
Group : SmallGroup(768,1088705)
Rank : 5
Schlafli Type : {2,4,12,4}
Number of vertices, edges, etc : 2, 4, 24, 24, 4
Order of s0s1s2s3s4 : 12
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 : {2,2,12,4}*384c, {2,4,6,4}*384b
4-fold quotients : {2,2,6,4}*192c
8-fold quotients : {2,2,3,4}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (51,63)(52,64)(53,65)(54,66)(55,67)(56,68)(57,69)(58,70)(59,71)(60,72)
(61,73)(62,74)(75,87)(76,88)(77,89)(78,90)(79,91)(80,92)(81,93)(82,94)(83,95)
(84,96)(85,97)(86,98);;
s2 := ( 3,51)( 4,53)( 5,52)( 6,54)( 7,59)( 8,61)( 9,60)(10,62)(11,55)(12,57)
(13,56)(14,58)(15,63)(16,65)(17,64)(18,66)(19,71)(20,73)(21,72)(22,74)(23,67)
(24,69)(25,68)(26,70)(27,75)(28,77)(29,76)(30,78)(31,83)(32,85)(33,84)(34,86)
(35,79)(36,81)(37,80)(38,82)(39,87)(40,89)(41,88)(42,90)(43,95)(44,97)(45,96)
(46,98)(47,91)(48,93)(49,92)(50,94);;
s3 := ( 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)(51,79)
(52,80)(53,82)(54,81)(55,75)(56,76)(57,78)(58,77)(59,83)(60,84)(61,86)(62,85)
(63,91)(64,92)(65,94)(66,93)(67,87)(68,88)(69,90)(70,89)(71,95)(72,96)(73,98)
(74,97);;
s4 := ( 3,30)( 4,29)( 5,28)( 6,27)( 7,34)( 8,33)( 9,32)(10,31)(11,38)(12,37)
(13,36)(14,35)(15,42)(16,41)(17,40)(18,39)(19,46)(20,45)(21,44)(22,43)(23,50)
(24,49)(25,48)(26,47)(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);;
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, s1*s2*s3*s2*s1*s2*s3*s2,
s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3,
s3*s2*s3*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(98)!(1,2);
s1 := Sym(98)!(51,63)(52,64)(53,65)(54,66)(55,67)(56,68)(57,69)(58,70)(59,71)
(60,72)(61,73)(62,74)(75,87)(76,88)(77,89)(78,90)(79,91)(80,92)(81,93)(82,94)
(83,95)(84,96)(85,97)(86,98);
s2 := Sym(98)!( 3,51)( 4,53)( 5,52)( 6,54)( 7,59)( 8,61)( 9,60)(10,62)(11,55)
(12,57)(13,56)(14,58)(15,63)(16,65)(17,64)(18,66)(19,71)(20,73)(21,72)(22,74)
(23,67)(24,69)(25,68)(26,70)(27,75)(28,77)(29,76)(30,78)(31,83)(32,85)(33,84)
(34,86)(35,79)(36,81)(37,80)(38,82)(39,87)(40,89)(41,88)(42,90)(43,95)(44,97)
(45,96)(46,98)(47,91)(48,93)(49,92)(50,94);
s3 := 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)
(51,79)(52,80)(53,82)(54,81)(55,75)(56,76)(57,78)(58,77)(59,83)(60,84)(61,86)
(62,85)(63,91)(64,92)(65,94)(66,93)(67,87)(68,88)(69,90)(70,89)(71,95)(72,96)
(73,98)(74,97);
s4 := Sym(98)!( 3,30)( 4,29)( 5,28)( 6,27)( 7,34)( 8,33)( 9,32)(10,31)(11,38)
(12,37)(13,36)(14,35)(15,42)(16,41)(17,40)(18,39)(19,46)(20,45)(21,44)(22,43)
(23,50)(24,49)(25,48)(26,47)(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);
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,
s1*s2*s3*s2*s1*s2*s3*s2, s3*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3,
s3*s2*s3*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s2 >;
to this polytope