Polytope of Type {2,4,6,4,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,6,4,2}*768a
if this polytope has a name.
Group : SmallGroup(768,1076475)
Rank : 6
Schlafli Type : {2,4,6,4,2}
Number of vertices, edges, etc : 2, 4, 12, 12, 4, 2
Order of s0s1s2s3s4s5 : 12
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Self-Dual
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 : {2,2,6,4,2}*384a, {2,4,6,2,2}*384a
3-fold quotients : {2,4,2,4,2}*256
4-fold quotients : {2,2,6,2,2}*192
6-fold quotients : {2,2,2,4,2}*128, {2,4,2,2,2}*128
8-fold quotients : {2,2,3,2,2}*96
12-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 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)(27,81)(28,82)(29,83)(30,84)(31,85)(32,86)(33,75)(34,76)
(35,77)(36,78)(37,79)(38,80)(39,93)(40,94)(41,95)(42,96)(43,97)(44,98)(45,87)
(46,88)(47,89)(48,90)(49,91)(50,92);;
s2 := ( 3,27)( 4,29)( 5,28)( 6,30)( 7,32)( 8,31)( 9,33)(10,35)(11,34)(12,36)
(13,38)(14,37)(15,45)(16,47)(17,46)(18,48)(19,50)(20,49)(21,39)(22,41)(23,40)
(24,42)(25,44)(26,43)(51,75)(52,77)(53,76)(54,78)(55,80)(56,79)(57,81)(58,83)
(59,82)(60,84)(61,86)(62,85)(63,93)(64,95)(65,94)(66,96)(67,98)(68,97)(69,87)
(70,89)(71,88)(72,90)(73,92)(74,91);;
s3 := ( 3, 4)( 6, 7)( 9,10)(12,13)(15,25)(16,24)(17,26)(18,22)(19,21)(20,23)
(27,28)(30,31)(33,34)(36,37)(39,49)(40,48)(41,50)(42,46)(43,45)(44,47)(51,52)
(54,55)(57,58)(60,61)(63,73)(64,72)(65,74)(66,70)(67,69)(68,71)(75,76)(78,79)
(81,82)(84,85)(87,97)(88,96)(89,98)(90,94)(91,93)(92,95);;
s4 := ( 3,63)( 4,64)( 5,65)( 6,66)( 7,67)( 8,68)( 9,69)(10,70)(11,71)(12,72)
(13,73)(14,74)(15,51)(16,52)(17,53)(18,54)(19,55)(20,56)(21,57)(22,58)(23,59)
(24,60)(25,61)(26,62)(27,93)(28,94)(29,95)(30,96)(31,97)(32,98)(33,87)(34,88)
(35,89)(36,90)(37,91)(38,92)(39,81)(40,82)(41,83)(42,84)(43,85)(44,86)(45,75)
(46,76)(47,77)(48,78)(49,79)(50,80);;
s5 := ( 99,100);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
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, s0*s5*s0*s5, s1*s5*s1*s5,
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(100)!(1,2);
s1 := Sym(100)!( 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)(27,81)(28,82)(29,83)(30,84)(31,85)(32,86)(33,75)
(34,76)(35,77)(36,78)(37,79)(38,80)(39,93)(40,94)(41,95)(42,96)(43,97)(44,98)
(45,87)(46,88)(47,89)(48,90)(49,91)(50,92);
s2 := Sym(100)!( 3,27)( 4,29)( 5,28)( 6,30)( 7,32)( 8,31)( 9,33)(10,35)(11,34)
(12,36)(13,38)(14,37)(15,45)(16,47)(17,46)(18,48)(19,50)(20,49)(21,39)(22,41)
(23,40)(24,42)(25,44)(26,43)(51,75)(52,77)(53,76)(54,78)(55,80)(56,79)(57,81)
(58,83)(59,82)(60,84)(61,86)(62,85)(63,93)(64,95)(65,94)(66,96)(67,98)(68,97)
(69,87)(70,89)(71,88)(72,90)(73,92)(74,91);
s3 := Sym(100)!( 3, 4)( 6, 7)( 9,10)(12,13)(15,25)(16,24)(17,26)(18,22)(19,21)
(20,23)(27,28)(30,31)(33,34)(36,37)(39,49)(40,48)(41,50)(42,46)(43,45)(44,47)
(51,52)(54,55)(57,58)(60,61)(63,73)(64,72)(65,74)(66,70)(67,69)(68,71)(75,76)
(78,79)(81,82)(84,85)(87,97)(88,96)(89,98)(90,94)(91,93)(92,95);
s4 := Sym(100)!( 3,63)( 4,64)( 5,65)( 6,66)( 7,67)( 8,68)( 9,69)(10,70)(11,71)
(12,72)(13,73)(14,74)(15,51)(16,52)(17,53)(18,54)(19,55)(20,56)(21,57)(22,58)
(23,59)(24,60)(25,61)(26,62)(27,93)(28,94)(29,95)(30,96)(31,97)(32,98)(33,87)
(34,88)(35,89)(36,90)(37,91)(38,92)(39,81)(40,82)(41,83)(42,84)(43,85)(44,86)
(45,75)(46,76)(47,77)(48,78)(49,79)(50,80);
s5 := Sym(100)!( 99,100);
poly := sub<Sym(100)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, 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, s0*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s4*s5*s4*s5, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope