Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,2,20,8}

Atlas Canonical Name {3,2,20,8}*1920a

Overview

Group
SmallGroup(1920,148893)
Rank
5
Schläfli Type
{3,2,20,8}
Vertices, edges, …
3, 3, 20, 80, 8
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)(25,28)(26,27)(30,33)(31,32)(35,38)(36,37)(40,43)(41,42)(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)(14,60)(15,59)(16,63)(17,62)(18,61)(19,55)(20,54)(21,58)(22,57)(23,56)(24,65)(25,64)(26,68)(27,67)(28,66)(29,70)(30,69)(31,73)(32,72)(33,71)(34,80)(35,79)(36,83)(37,82)(38,81)(39,75)(40,74)(41,78)(42,77)(43,76);;
s4 := (14,19)(15,20)(16,21)(17,22)(18,23)(34,39)(35,40)(36,41)(37,42)(38,43)(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*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)(25,28)(26,27)(30,33)(31,32)(35,38)(36,37)(40,43)(41,42)(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)(14,60)(15,59)(16,63)(17,62)(18,61)(19,55)(20,54)(21,58)(22,57)(23,56)(24,65)(25,64)(26,68)(27,67)(28,66)(29,70)(30,69)(31,73)(32,72)(33,71)(34,80)(35,79)(36,83)(37,82)(38,81)(39,75)(40,74)(41,78)(42,77)(43,76);
s4 := Sym(83)!(14,19)(15,20)(16,21)(17,22)(18,23)(34,39)(35,40)(36,41)(37,42)(38,43)(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*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 >;