Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,2,40,4}

Atlas Canonical Name {3,2,40,4}*1920a

Overview

Group
SmallGroup(1920,148902)
Rank
5
Schläfli Type
{3,2,40,4}
Vertices, edges, …
3, 3, 40, 80, 4
Order of s0s1s2s3s4
120
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

5-fold

8-fold

10-fold

16-fold

20-fold

40-fold

Covers minimal covers in bold

None in this atlas.

Representations

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