Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,6,4}

Atlas Canonical Name {2,6,4}*768b

Overview

Group
SmallGroup(768,1089358)
Rank
4
Schläfli Type
{2,6,4}
Vertices, edges, …
2, 48, 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

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