Part of the Atlas of Small Regular Polytopes

Polytope of Type {20,4,2}

Atlas Canonical Name {20,4,2}*1440

Overview

Group
SmallGroup(1440,5890)
Rank
4
Schläfli Type
{20,4,2}
Vertices, edges, …
90, 180, 18, 2
Order of s0s1s2s3
30
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

5-fold

10-fold

18-fold

36-fold

90-fold

Covers minimal covers in bold

None in this atlas.

Representations

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