Polytope of Type {2,8,6,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,6,3}*768
if this polytope has a name.
Group : SmallGroup(768,1089270)
Rank : 5
Schlafli Type : {2,8,6,3}
Number of vertices, edges, etc : 2, 8, 32, 12, 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
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 := (27,39)(28,40)(29,41)(30,42)(31,43)(32,44)(33,45)(34,46)(35,47)(36,48)
(37,49)(38,50)(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)( 4,53)( 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)(27,87)(28,89)(29,88)(30,90)(31,95)(32,97)(33,96)(34,98)
(35,91)(36,93)(37,92)(38,94)(39,75)(40,77)(41,76)(42,78)(43,83)(44,85)(45,84)
(46,86)(47,79)(48,81)(49,80)(50,82);;
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)(51,55)
(52,56)(53,58)(54,57)(61,62)(63,67)(64,68)(65,70)(66,69)(73,74)(75,79)(76,80)
(77,82)(78,81)(85,86)(87,91)(88,92)(89,94)(90,93)(97,98);;
s4 := ( 3, 6)( 7,14)( 8,12)( 9,13)(10,11)(15,18)(19,26)(20,24)(21,25)(22,23)
(27,30)(31,38)(32,36)(33,37)(34,35)(39,42)(43,50)(44,48)(45,49)(46,47)(51,54)
(55,62)(56,60)(57,61)(58,59)(63,66)(67,74)(68,72)(69,73)(70,71)(75,78)(79,86)
(80,84)(81,85)(82,83)(87,90)(91,98)(92,96)(93,97)(94,95);;
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,
s3*s4*s3*s4*s3*s4, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s4*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3,
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(98)!(1,2);
s1 := Sym(98)!(27,39)(28,40)(29,41)(30,42)(31,43)(32,44)(33,45)(34,46)(35,47)
(36,48)(37,49)(38,50)(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)( 4,53)( 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)(27,87)(28,89)(29,88)(30,90)(31,95)(32,97)(33,96)
(34,98)(35,91)(36,93)(37,92)(38,94)(39,75)(40,77)(41,76)(42,78)(43,83)(44,85)
(45,84)(46,86)(47,79)(48,81)(49,80)(50,82);
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)
(51,55)(52,56)(53,58)(54,57)(61,62)(63,67)(64,68)(65,70)(66,69)(73,74)(75,79)
(76,80)(77,82)(78,81)(85,86)(87,91)(88,92)(89,94)(90,93)(97,98);
s4 := Sym(98)!( 3, 6)( 7,14)( 8,12)( 9,13)(10,11)(15,18)(19,26)(20,24)(21,25)
(22,23)(27,30)(31,38)(32,36)(33,37)(34,35)(39,42)(43,50)(44,48)(45,49)(46,47)
(51,54)(55,62)(56,60)(57,61)(58,59)(63,66)(67,74)(68,72)(69,73)(70,71)(75,78)
(79,86)(80,84)(81,85)(82,83)(87,90)(91,98)(92,96)(93,97)(94,95);
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, s3*s4*s3*s4*s3*s4,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s4*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3,
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 >;
to this polytope