Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,8,6}

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

Overview

Group
SmallGroup(768,1089270)
Rank
4
Schläfli Type
{2,8,6}
Vertices, edges, …
2, 32, 96, 24
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 := ( 3, 5)( 4, 6)( 7, 9)( 8,10)(11,13)(12,14)(15,17)(16,18)(19,21)(20,22)(23,25)(24,26)(27,41)(28,42)(29,39)(30,40)(31,45)(32,46)(33,43)(34,44)(35,49)(36,50)(37,47)(38,48)(51,77)(52,78)(53,75)(54,76)(55,81)(56,82)(57,79)(58,80)(59,85)(60,86)(61,83)(62,84)(63,89)(64,90)(65,87)(66,88)(67,93)(68,94)(69,91)(70,92)(71,97)(72,98)(73,95)(74,96);;
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 := ( 3,11)( 4,14)( 5,13)( 6,12)( 8,10)(15,23)(16,26)(17,25)(18,24)(20,22)(27,35)(28,38)(29,37)(30,36)(32,34)(39,47)(40,50)(41,49)(42,48)(44,46)(51,59)(52,62)(53,61)(54,60)(56,58)(63,71)(64,74)(65,73)(66,72)(68,70)(75,83)(76,86)(77,85)(78,84)(80,82)(87,95)(88,98)(89,97)(90,96)(92,94);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(98)!(1,2);
s1 := Sym(98)!( 3, 5)( 4, 6)( 7, 9)( 8,10)(11,13)(12,14)(15,17)(16,18)(19,21)(20,22)(23,25)(24,26)(27,41)(28,42)(29,39)(30,40)(31,45)(32,46)(33,43)(34,44)(35,49)(36,50)(37,47)(38,48)(51,77)(52,78)(53,75)(54,76)(55,81)(56,82)(57,79)(58,80)(59,85)(60,86)(61,83)(62,84)(63,89)(64,90)(65,87)(66,88)(67,93)(68,94)(69,91)(70,92)(71,97)(72,98)(73,95)(74,96);
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)!( 3,11)( 4,14)( 5,13)( 6,12)( 8,10)(15,23)(16,26)(17,25)(18,24)(20,22)(27,35)(28,38)(29,37)(30,36)(32,34)(39,47)(40,50)(41,49)(42,48)(44,46)(51,59)(52,62)(53,61)(54,60)(56,58)(63,71)(64,74)(65,73)(66,72)(68,70)(75,83)(76,86)(77,85)(78,84)(80,82)(87,95)(88,98)(89,97)(90,96)(92,94);
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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2 >;