Part of the Atlas of Small Regular Polytopes

Polytope of Type {20,4,2}

Atlas Canonical Name {20,4,2}*1920c

Overview

Group
SmallGroup(1920,240809)
Rank
4
Schläfli Type
{20,4,2}
Vertices, edges, …
120, 240, 24, 2
Order of s0s1s2s3
24
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

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