Polytope of Type {3,6,8,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,6,8,2}*768
if this polytope has a name.
Group : SmallGroup(768,1089270)
Rank : 5
Schlafli Type : {3,6,8,2}
Number of vertices, edges, etc : 4, 12, 32, 8, 2
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 : {3,6,4,2}*384
4-fold quotients : {3,6,2,2}*192
8-fold quotients : {3,3,2,2}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(17,21)(18,23)(19,22)(20,24)
(26,27)(29,33)(30,35)(31,34)(32,36)(38,39)(41,45)(42,47)(43,46)(44,48)(50,51)
(53,57)(54,59)(55,58)(56,60)(62,63)(65,69)(66,71)(67,70)(68,72)(74,75)(77,81)
(78,83)(79,82)(80,84)(86,87)(89,93)(90,95)(91,94)(92,96);;
s1 := ( 1, 5)( 2, 6)( 3, 8)( 4, 7)(11,12)(13,17)(14,18)(15,20)(16,19)(23,24)
(25,29)(26,30)(27,32)(28,31)(35,36)(37,41)(38,42)(39,44)(40,43)(47,48)(49,53)
(50,54)(51,56)(52,55)(59,60)(61,65)(62,66)(63,68)(64,67)(71,72)(73,77)(74,78)
(75,80)(76,79)(83,84)(85,89)(86,90)(87,92)(88,91)(95,96);;
s2 := ( 1, 4)( 5,12)( 6,10)( 7,11)( 8, 9)(13,16)(17,24)(18,22)(19,23)(20,21)
(25,40)(26,38)(27,39)(28,37)(29,48)(30,46)(31,47)(32,45)(33,44)(34,42)(35,43)
(36,41)(49,76)(50,74)(51,75)(52,73)(53,84)(54,82)(55,83)(56,81)(57,80)(58,78)
(59,79)(60,77)(61,88)(62,86)(63,87)(64,85)(65,96)(66,94)(67,95)(68,93)(69,92)
(70,90)(71,91)(72,89);;
s3 := ( 1,49)( 2,50)( 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)(25,85)(26,86)(27,87)(28,88)(29,89)(30,90)(31,91)(32,92)
(33,93)(34,94)(35,95)(36,96)(37,73)(38,74)(39,75)(40,76)(41,77)(42,78)(43,79)
(44,80)(45,81)(46,82)(47,83)(48,84);;
s4 := (97,98);;
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*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,
s0*s1*s0*s1*s0*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(98)!( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(17,21)(18,23)(19,22)
(20,24)(26,27)(29,33)(30,35)(31,34)(32,36)(38,39)(41,45)(42,47)(43,46)(44,48)
(50,51)(53,57)(54,59)(55,58)(56,60)(62,63)(65,69)(66,71)(67,70)(68,72)(74,75)
(77,81)(78,83)(79,82)(80,84)(86,87)(89,93)(90,95)(91,94)(92,96);
s1 := Sym(98)!( 1, 5)( 2, 6)( 3, 8)( 4, 7)(11,12)(13,17)(14,18)(15,20)(16,19)
(23,24)(25,29)(26,30)(27,32)(28,31)(35,36)(37,41)(38,42)(39,44)(40,43)(47,48)
(49,53)(50,54)(51,56)(52,55)(59,60)(61,65)(62,66)(63,68)(64,67)(71,72)(73,77)
(74,78)(75,80)(76,79)(83,84)(85,89)(86,90)(87,92)(88,91)(95,96);
s2 := Sym(98)!( 1, 4)( 5,12)( 6,10)( 7,11)( 8, 9)(13,16)(17,24)(18,22)(19,23)
(20,21)(25,40)(26,38)(27,39)(28,37)(29,48)(30,46)(31,47)(32,45)(33,44)(34,42)
(35,43)(36,41)(49,76)(50,74)(51,75)(52,73)(53,84)(54,82)(55,83)(56,81)(57,80)
(58,78)(59,79)(60,77)(61,88)(62,86)(63,87)(64,85)(65,96)(66,94)(67,95)(68,93)
(69,92)(70,90)(71,91)(72,89);
s3 := Sym(98)!( 1,49)( 2,50)( 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)(25,85)(26,86)(27,87)(28,88)(29,89)(30,90)(31,91)
(32,92)(33,93)(34,94)(35,95)(36,96)(37,73)(38,74)(39,75)(40,76)(41,77)(42,78)
(43,79)(44,80)(45,81)(46,82)(47,83)(48,84);
s4 := Sym(98)!(97,98);
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*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, s0*s1*s0*s1*s0*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope