Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,6,8}

Atlas Canonical Name {2,6,8}*384b

Overview

Group
SmallGroup(384,20062)
Rank
4
Schläfli Type
{2,6,8}
Vertices, edges, …
2, 12, 48, 16
Order of s0s1s2s3
12
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

24-fold

Covers minimal covers in bold

2-fold

3-fold

5-fold

Representations

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