Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,2,4,20}

Atlas Canonical Name {3,2,4,20}*960

Overview

Group
SmallGroup(960,7401)
Rank
5
Schläfli Type
{3,2,4,20}
Vertices, edges, …
3, 3, 4, 40, 20
Order of s0s1s2s3s4
60
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

20-fold

Covers minimal covers in bold

2-fold

Representations

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