Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(960,7401)
Rank
5
Schläfli Type
{3,2,20,4}
Vertices, edges, …
3, 3, 20, 40, 4
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 := ( 5, 8)( 6, 7)(10,13)(11,12)(15,18)(16,17)(20,23)(21,22)(24,34)(25,38)(26,37)(27,36)(28,35)(29,39)(30,43)(31,42)(32,41)(33,40)(45,48)(46,47)(50,53)(51,52)(55,58)(56,57)(60,63)(61,62)(64,74)(65,78)(66,77)(67,76)(68,75)(69,79)(70,83)(71,82)(72,81)(73,80);;
s3 := ( 4,25)( 5,24)( 6,28)( 7,27)( 8,26)( 9,30)(10,29)(11,33)(12,32)(13,31)(14,35)(15,34)(16,38)(17,37)(18,36)(19,40)(20,39)(21,43)(22,42)(23,41)(44,65)(45,64)(46,68)(47,67)(48,66)(49,70)(50,69)(51,73)(52,72)(53,71)(54,75)(55,74)(56,78)(57,77)(58,76)(59,80)(60,79)(61,83)(62,82)(63,81);;
s4 := ( 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);;
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 ];;
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)(24,34)(25,38)(26,37)(27,36)(28,35)(29,39)(30,43)(31,42)(32,41)(33,40)(45,48)(46,47)(50,53)(51,52)(55,58)(56,57)(60,63)(61,62)(64,74)(65,78)(66,77)(67,76)(68,75)(69,79)(70,83)(71,82)(72,81)(73,80);
s3 := Sym(83)!( 4,25)( 5,24)( 6,28)( 7,27)( 8,26)( 9,30)(10,29)(11,33)(12,32)(13,31)(14,35)(15,34)(16,38)(17,37)(18,36)(19,40)(20,39)(21,43)(22,42)(23,41)(44,65)(45,64)(46,68)(47,67)(48,66)(49,70)(50,69)(51,73)(52,72)(53,71)(54,75)(55,74)(56,78)(57,77)(58,76)(59,80)(60,79)(61,83)(62,82)(63,81);
s4 := 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);
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 >;