Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,6,8}

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

Overview

Group
SmallGroup(768,1089270)
Rank
4
Schläfli Type
{2,6,8}
Vertices, edges, …
2, 24, 96, 32
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 := (1,2);;
s1 := ( 4, 5)( 7,11)( 8,13)( 9,12)(10,14)(16,17)(19,23)(20,25)(21,24)(22,26)(28,29)(31,35)(32,37)(33,36)(34,38)(40,41)(43,47)(44,49)(45,48)(46,50)(52,53)(55,59)(56,61)(57,60)(58,62)(64,65)(67,71)(68,73)(69,72)(70,74)(76,77)(79,83)(80,85)(81,84)(82,86)(88,89)(91,95)(92,97)(93,96)(94,98);;
s2 := ( 3, 7)( 4, 8)( 5,10)( 6, 9)(13,14)(15,19)(16,20)(17,22)(18,21)(25,26)(27,43)(28,44)(29,46)(30,45)(31,39)(32,40)(33,42)(34,41)(35,47)(36,48)(37,50)(38,49)(51,79)(52,80)(53,82)(54,81)(55,75)(56,76)(57,78)(58,77)(59,83)(60,84)(61,86)(62,85)(63,91)(64,92)(65,94)(66,93)(67,87)(68,88)(69,90)(70,89)(71,95)(72,96)(73,98)(74,97);;
s3 := ( 3,54)( 4,53)( 5,52)( 6,51)( 7,58)( 8,57)( 9,56)(10,55)(11,62)(12,61)(13,60)(14,59)(15,66)(16,65)(17,64)(18,63)(19,70)(20,69)(21,68)(22,67)(23,74)(24,73)(25,72)(26,71)(27,90)(28,89)(29,88)(30,87)(31,94)(32,93)(33,92)(34,91)(35,98)(36,97)(37,96)(38,95)(39,78)(40,77)(41,76)(42,75)(43,82)(44,81)(45,80)(46,79)(47,86)(48,85)(49,84)(50,83);;
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*s3*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
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)!(1,2);
s1 := Sym(98)!( 4, 5)( 7,11)( 8,13)( 9,12)(10,14)(16,17)(19,23)(20,25)(21,24)(22,26)(28,29)(31,35)(32,37)(33,36)(34,38)(40,41)(43,47)(44,49)(45,48)(46,50)(52,53)(55,59)(56,61)(57,60)(58,62)(64,65)(67,71)(68,73)(69,72)(70,74)(76,77)(79,83)(80,85)(81,84)(82,86)(88,89)(91,95)(92,97)(93,96)(94,98);
s2 := Sym(98)!( 3, 7)( 4, 8)( 5,10)( 6, 9)(13,14)(15,19)(16,20)(17,22)(18,21)(25,26)(27,43)(28,44)(29,46)(30,45)(31,39)(32,40)(33,42)(34,41)(35,47)(36,48)(37,50)(38,49)(51,79)(52,80)(53,82)(54,81)(55,75)(56,76)(57,78)(58,77)(59,83)(60,84)(61,86)(62,85)(63,91)(64,92)(65,94)(66,93)(67,87)(68,88)(69,90)(70,89)(71,95)(72,96)(73,98)(74,97);
s3 := Sym(98)!( 3,54)( 4,53)( 5,52)( 6,51)( 7,58)( 8,57)( 9,56)(10,55)(11,62)(12,61)(13,60)(14,59)(15,66)(16,65)(17,64)(18,63)(19,70)(20,69)(21,68)(22,67)(23,74)(24,73)(25,72)(26,71)(27,90)(28,89)(29,88)(30,87)(31,94)(32,93)(33,92)(34,91)(35,98)(36,97)(37,96)(38,95)(39,78)(40,77)(41,76)(42,75)(43,82)(44,81)(45,80)(46,79)(47,86)(48,85)(49,84)(50,83);
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*s3*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;