Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1920,240988)
Rank
5
Schläfli Type
{20,3,2,2}
Vertices, edges, …
80, 120, 12, 2, 2
Order of s0s1s2s3s4
20
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

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := ( 2,10)( 3,12)( 4,17)( 5,19)( 7,38)(11,28)(13,44)(14,43)(15,34)(20,23)(21,36)(22,37)(24,26)(29,33)(30,31)(32,35)(39,47)(40,46)(41,45)(42,48);;
s1 := ( 1, 4)( 2,13)( 3, 8)( 5,16)( 6,17)( 7,43)( 9,30)(10,35)(11,27)(12,22)(14,24)(15,25)(18,19)(20,46)(21,28)(23,33)(26,29)(31,40)(32,39)(34,42)(36,38)(37,47)(41,44)(45,48);;
s2 := ( 1, 9)( 2,19)( 3,13)( 4,24)( 5,10)( 6,27)( 7,37)( 8,18)(11,29)(12,44)(14,30)(15,35)(16,25)(17,26)(20,42)(21,45)(22,38)(23,48)(28,33)(31,43)(32,34)(36,41)(39,46)(40,47);;
s3 := (49,50);;
s4 := (51,52);;
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(52)!( 2,10)( 3,12)( 4,17)( 5,19)( 7,38)(11,28)(13,44)(14,43)(15,34)(20,23)(21,36)(22,37)(24,26)(29,33)(30,31)(32,35)(39,47)(40,46)(41,45)(42,48);
s1 := Sym(52)!( 1, 4)( 2,13)( 3, 8)( 5,16)( 6,17)( 7,43)( 9,30)(10,35)(11,27)(12,22)(14,24)(15,25)(18,19)(20,46)(21,28)(23,33)(26,29)(31,40)(32,39)(34,42)(36,38)(37,47)(41,44)(45,48);
s2 := Sym(52)!( 1, 9)( 2,19)( 3,13)( 4,24)( 5,10)( 6,27)( 7,37)( 8,18)(11,29)(12,44)(14,30)(15,35)(16,25)(17,26)(20,42)(21,45)(22,38)(23,48)(28,33)(31,43)(32,34)(36,41)(39,46)(40,47);
s3 := Sym(52)!(49,50);
s4 := Sym(52)!(51,52);
poly := sub<Sym(52)|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, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1 >;