Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,8,2}

Atlas Canonical Name {6,8,2}*768g

Overview

Group
SmallGroup(768,1089270)
Rank
4
Schläfli Type
{6,8,2}
Vertices, edges, …
24, 96, 32, 2
Order of s0s1s2s3
24
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

12-fold

16-fold

24-fold

32-fold

48-fold

Covers minimal covers in bold

None in this atlas.

Representations

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)(25,41)(26,42)(27,44)(28,43)(29,37)(30,38)(31,40)(32,39)(33,45)(34,46)(35,48)(36,47)(49,77)(50,78)(51,80)(52,79)(53,73)(54,74)(55,76)(56,75)(57,81)(58,82)(59,84)(60,83)(61,89)(62,90)(63,92)(64,91)(65,85)(66,86)(67,88)(68,87)(69,93)(70,94)(71,96)(72,95);;
s2 := ( 1,52)( 2,51)( 3,50)( 4,49)( 5,56)( 6,55)( 7,54)( 8,53)( 9,60)(10,59)(11,58)(12,57)(13,64)(14,63)(15,62)(16,61)(17,68)(18,67)(19,66)(20,65)(21,72)(22,71)(23,70)(24,69)(25,88)(26,87)(27,86)(28,85)(29,92)(30,91)(31,90)(32,89)(33,96)(34,95)(35,94)(36,93)(37,76)(38,75)(39,74)(40,73)(41,80)(42,79)(43,78)(44,77)(45,84)(46,83)(47,82)(48,81);;
s3 := (97,98);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
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)!( 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)(25,41)(26,42)(27,44)(28,43)(29,37)(30,38)(31,40)(32,39)(33,45)(34,46)(35,48)(36,47)(49,77)(50,78)(51,80)(52,79)(53,73)(54,74)(55,76)(56,75)(57,81)(58,82)(59,84)(60,83)(61,89)(62,90)(63,92)(64,91)(65,85)(66,86)(67,88)(68,87)(69,93)(70,94)(71,96)(72,95);
s2 := Sym(98)!( 1,52)( 2,51)( 3,50)( 4,49)( 5,56)( 6,55)( 7,54)( 8,53)( 9,60)(10,59)(11,58)(12,57)(13,64)(14,63)(15,62)(16,61)(17,68)(18,67)(19,66)(20,65)(21,72)(22,71)(23,70)(24,69)(25,88)(26,87)(27,86)(28,85)(29,92)(30,91)(31,90)(32,89)(33,96)(34,95)(35,94)(36,93)(37,76)(38,75)(39,74)(40,73)(41,80)(42,79)(43,78)(44,77)(45,84)(46,83)(47,82)(48,81);
s3 := Sym(98)!(97,98);
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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;