Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,20,2}

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

Overview

Group
SmallGroup(1920,240809)
Rank
4
Schläfli Type
{4,20,2}
Vertices, edges, …
24, 240, 120, 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 := ( 1,12)( 2,10)( 3,15)( 4,37)( 5,44)( 6,20)( 7,17)( 8,48)( 9,29)(11,21)(13,28)(14,40)(16,41)(18,46)(19,32)(22,26)(23,25)(24,31)(27,39)(30,45)(33,38)(34,47)(35,36)(42,43);;
s1 := ( 1, 3)( 2,21)( 4,48)( 5,32)( 6, 9)( 7,40)( 8,14)(10,36)(11,25)(12,20)(13,39)(15,29)(16,31)(17,37)(18,38)(19,33)(22,47)(23,35)(24,43)(26,34)(27,28)(30,42)(41,45)(44,46);;
s2 := ( 1, 8)( 2,43)( 4,30)( 5,13)( 6,24)( 7,47)( 9,22)(10,42)(11,38)(12,48)(16,32)(17,34)(19,41)(20,31)(21,33)(26,29)(27,36)(28,44)(35,39)(37,45);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(50)!( 1,12)( 2,10)( 3,15)( 4,37)( 5,44)( 6,20)( 7,17)( 8,48)( 9,29)(11,21)(13,28)(14,40)(16,41)(18,46)(19,32)(22,26)(23,25)(24,31)(27,39)(30,45)(33,38)(34,47)(35,36)(42,43);
s1 := Sym(50)!( 1, 3)( 2,21)( 4,48)( 5,32)( 6, 9)( 7,40)( 8,14)(10,36)(11,25)(12,20)(13,39)(15,29)(16,31)(17,37)(18,38)(19,33)(22,47)(23,35)(24,43)(26,34)(27,28)(30,42)(41,45)(44,46);
s2 := Sym(50)!( 1, 8)( 2,43)( 4,30)( 5,13)( 6,24)( 7,47)( 9,22)(10,42)(11,38)(12,48)(16,32)(17,34)(19,41)(20,31)(21,33)(26,29)(27,36)(28,44)(35,39)(37,45);
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, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2 >;