Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,6,8}

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

Overview

Group
SmallGroup(768,1089093)
Rank
4
Schläfli Type
{2,6,8}
Vertices, edges, …
2, 24, 96, 32
Order of s0s1s2s3
6
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

16-fold

32-fold

48-fold

Covers minimal covers in bold

None in this atlas.

Representations

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