Polytope of Type {2,8,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,6}*384b
if this polytope has a name.
Group : SmallGroup(384,20062)
Rank : 4
Schlafli Type : {2,8,6}
Number of vertices, edges, etc : 2, 16, 48, 12
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,8,6,2} of size 768
Vertex Figure Of :
{2,2,8,6} of size 768
{3,2,8,6} of size 1152
{5,2,8,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,8,3}*192, {2,4,6}*192
4-fold quotients : {2,4,3}*96, {2,4,6}*96b, {2,4,6}*96c
8-fold quotients : {2,4,3}*48, {2,2,6}*48
16-fold quotients : {2,2,3}*24
24-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,8,12}*768e, {4,8,6}*768c, {2,8,6}*768f, {2,8,12}*768h
3-fold covers : {2,8,18}*1152b, {2,24,6}*1152b, {6,8,6}*1152a, {2,24,6}*1152e
5-fold covers : {10,8,6}*1920a, {2,40,6}*1920c, {2,8,30}*1920b
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3,29)( 4,30)( 5,28)( 6,27)( 7,33)( 8,34)( 9,32)(10,31)(11,37)(12,38)
(13,36)(14,35)(15,41)(16,42)(17,40)(18,39)(19,45)(20,46)(21,44)(22,43)(23,49)
(24,50)(25,48)(26,47)(51,77)(52,78)(53,76)(54,75)(55,81)(56,82)(57,80)(58,79)
(59,85)(60,86)(61,84)(62,83)(63,89)(64,90)(65,88)(66,87)(67,93)(68,94)(69,92)
(70,91)(71,97)(72,98)(73,96)(74,95);;
s2 := ( 5, 7)( 6, 8)( 9,10)(11,19)(12,20)(13,23)(14,24)(15,21)(16,22)(17,26)
(18,25)(27,28)(29,32)(30,31)(35,44)(36,43)(37,48)(38,47)(39,46)(40,45)(41,49)
(42,50)(53,55)(54,56)(57,58)(59,67)(60,68)(61,71)(62,72)(63,69)(64,70)(65,74)
(66,73)(75,76)(77,80)(78,79)(83,92)(84,91)(85,96)(86,95)(87,94)(88,93)(89,97)
(90,98);;
s3 := ( 3,59)( 4,60)( 5,62)( 6,61)( 7,65)( 8,66)( 9,63)(10,64)(11,51)(12,52)
(13,54)(14,53)(15,57)(16,58)(17,55)(18,56)(19,67)(20,68)(21,70)(22,69)(23,73)
(24,74)(25,71)(26,72)(27,84)(28,83)(29,85)(30,86)(31,90)(32,89)(33,88)(34,87)
(35,76)(36,75)(37,77)(38,78)(39,82)(40,81)(41,80)(42,79)(43,92)(44,91)(45,93)
(46,94)(47,98)(48,97)(49,96)(50,95);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(98)!(1,2);
s1 := Sym(98)!( 3,29)( 4,30)( 5,28)( 6,27)( 7,33)( 8,34)( 9,32)(10,31)(11,37)
(12,38)(13,36)(14,35)(15,41)(16,42)(17,40)(18,39)(19,45)(20,46)(21,44)(22,43)
(23,49)(24,50)(25,48)(26,47)(51,77)(52,78)(53,76)(54,75)(55,81)(56,82)(57,80)
(58,79)(59,85)(60,86)(61,84)(62,83)(63,89)(64,90)(65,88)(66,87)(67,93)(68,94)
(69,92)(70,91)(71,97)(72,98)(73,96)(74,95);
s2 := Sym(98)!( 5, 7)( 6, 8)( 9,10)(11,19)(12,20)(13,23)(14,24)(15,21)(16,22)
(17,26)(18,25)(27,28)(29,32)(30,31)(35,44)(36,43)(37,48)(38,47)(39,46)(40,45)
(41,49)(42,50)(53,55)(54,56)(57,58)(59,67)(60,68)(61,71)(62,72)(63,69)(64,70)
(65,74)(66,73)(75,76)(77,80)(78,79)(83,92)(84,91)(85,96)(86,95)(87,94)(88,93)
(89,97)(90,98);
s3 := Sym(98)!( 3,59)( 4,60)( 5,62)( 6,61)( 7,65)( 8,66)( 9,63)(10,64)(11,51)
(12,52)(13,54)(14,53)(15,57)(16,58)(17,55)(18,56)(19,67)(20,68)(21,70)(22,69)
(23,73)(24,74)(25,71)(26,72)(27,84)(28,83)(29,85)(30,86)(31,90)(32,89)(33,88)
(34,87)(35,76)(36,75)(37,77)(38,78)(39,82)(40,81)(41,80)(42,79)(43,92)(44,91)
(45,93)(46,94)(47,98)(48,97)(49,96)(50,95);
poly := sub<Sym(98)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2 >;
to this polytope