Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,3,6,4}

Atlas Canonical Name {2,3,6,4}*768b

Overview

Group
SmallGroup(768,1089108)
Rank
5
Schläfli Type
{2,3,6,4}
Vertices, edges, …
2, 4, 24, 32, 8
Order of s0s1s2s3s4
4
Order of s0s1s2s3s4s3s2s1
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

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := ( 5, 6)( 7,11)( 8,12)( 9,14)(10,13)(17,18)(19,35)(20,36)(21,38)(22,37)(23,43)(24,44)(25,46)(26,45)(27,39)(28,40)(29,42)(30,41)(31,47)(32,48)(33,50)(34,49)(53,54)(55,59)(56,60)(57,62)(58,61)(65,66)(67,83)(68,84)(69,86)(70,85)(71,91)(72,92)(73,94)(74,93)(75,87)(76,88)(77,90)(78,89)(79,95)(80,96)(81,98)(82,97);;
s2 := ( 3,19)( 4,22)( 5,21)( 6,20)( 7,23)( 8,26)( 9,25)(10,24)(11,31)(12,34)(13,33)(14,32)(15,27)(16,30)(17,29)(18,28)(36,38)(40,42)(43,47)(44,50)(45,49)(46,48)(51,67)(52,70)(53,69)(54,68)(55,71)(56,74)(57,73)(58,72)(59,79)(60,82)(61,81)(62,80)(63,75)(64,78)(65,77)(66,76)(84,86)(88,90)(91,95)(92,98)(93,97)(94,96);;
s3 := ( 3,63)( 4,64)( 5,66)( 6,65)( 7,55)( 8,56)( 9,58)(10,57)(11,59)(12,60)(13,62)(14,61)(15,51)(16,52)(17,54)(18,53)(19,95)(20,96)(21,98)(22,97)(23,87)(24,88)(25,90)(26,89)(27,91)(28,92)(29,94)(30,93)(31,83)(32,84)(33,86)(34,85)(35,79)(36,80)(37,82)(38,81)(39,71)(40,72)(41,74)(42,73)(43,75)(44,76)(45,78)(46,77)(47,67)(48,68)(49,70)(50,69);;
s4 := ( 7, 9)( 8,10)(11,14)(12,13)(15,16)(17,18)(23,25)(24,26)(27,30)(28,29)(31,32)(33,34)(39,41)(40,42)(43,46)(44,45)(47,48)(49,50)(55,57)(56,58)(59,62)(60,61)(63,64)(65,66)(71,73)(72,74)(75,78)(76,77)(79,80)(81,82)(87,89)(88,90)(91,94)(92,93)(95,96)(97,98);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s1*s2*s1*s2*s1*s2, s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s2*s3*s2*s3*s4*s3*s2*s3*s2*s3*s4*s3, 
s3*s1*s4*s2*s1*s3*s4*s2*s3*s1*s4*s2*s3*s1*s4*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(98)!(1,2);
s1 := Sym(98)!( 5, 6)( 7,11)( 8,12)( 9,14)(10,13)(17,18)(19,35)(20,36)(21,38)(22,37)(23,43)(24,44)(25,46)(26,45)(27,39)(28,40)(29,42)(30,41)(31,47)(32,48)(33,50)(34,49)(53,54)(55,59)(56,60)(57,62)(58,61)(65,66)(67,83)(68,84)(69,86)(70,85)(71,91)(72,92)(73,94)(74,93)(75,87)(76,88)(77,90)(78,89)(79,95)(80,96)(81,98)(82,97);
s2 := Sym(98)!( 3,19)( 4,22)( 5,21)( 6,20)( 7,23)( 8,26)( 9,25)(10,24)(11,31)(12,34)(13,33)(14,32)(15,27)(16,30)(17,29)(18,28)(36,38)(40,42)(43,47)(44,50)(45,49)(46,48)(51,67)(52,70)(53,69)(54,68)(55,71)(56,74)(57,73)(58,72)(59,79)(60,82)(61,81)(62,80)(63,75)(64,78)(65,77)(66,76)(84,86)(88,90)(91,95)(92,98)(93,97)(94,96);
s3 := Sym(98)!( 3,63)( 4,64)( 5,66)( 6,65)( 7,55)( 8,56)( 9,58)(10,57)(11,59)(12,60)(13,62)(14,61)(15,51)(16,52)(17,54)(18,53)(19,95)(20,96)(21,98)(22,97)(23,87)(24,88)(25,90)(26,89)(27,91)(28,92)(29,94)(30,93)(31,83)(32,84)(33,86)(34,85)(35,79)(36,80)(37,82)(38,81)(39,71)(40,72)(41,74)(42,73)(43,75)(44,76)(45,78)(46,77)(47,67)(48,68)(49,70)(50,69);
s4 := Sym(98)!( 7, 9)( 8,10)(11,14)(12,13)(15,16)(17,18)(23,25)(24,26)(27,30)(28,29)(31,32)(33,34)(39,41)(40,42)(43,46)(44,45)(47,48)(49,50)(55,57)(56,58)(59,62)(60,61)(63,64)(65,66)(71,73)(72,74)(75,78)(76,77)(79,80)(81,82)(87,89)(88,90)(91,94)(92,93)(95,96)(97,98);
poly := sub<Sym(98)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s2*s3*s2*s3*s4*s3*s2*s3*s2*s3*s4*s3, 
s3*s1*s4*s2*s1*s3*s4*s2*s3*s1*s4*s2*s3*s1*s4*s2 >;