Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,8,4,3}

Atlas Canonical Name {2,8,4,3}*768

Overview

Group
SmallGroup(768,1089270)
Rank
5
Schläfli Type
{2,8,4,3}
Vertices, edges, …
2, 8, 32, 12, 6
Order of s0s1s2s3s4
24
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

16-fold

Covers minimal covers in bold

None in this atlas.

Representations

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