Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,20,4}

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

Overview

Group
SmallGroup(1440,5890)
Rank
4
Schläfli Type
{2,20,4}
Vertices, edges, …
2, 90, 180, 18
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 := (1,2);;
s1 := ( 4, 7)( 5, 6)( 8,38)( 9,42)(10,41)(11,40)(12,39)(13,28)(14,32)(15,31)(16,30)(17,29)(18,33)(19,37)(20,36)(21,35)(22,34)(24,27)(25,26)(44,47)(45,46);;
s2 := ( 3, 4)( 5, 7)( 8, 9)(10,12)(13,14)(15,17)(18,44)(19,43)(20,47)(21,46)(22,45)(23,34)(24,33)(25,37)(26,36)(27,35)(28,39)(29,38)(30,42)(31,41)(32,40);;
s3 := ( 3,23)( 4,24)( 5,25)( 6,26)( 7,27)( 8,33)( 9,34)(10,35)(11,36)(12,37)(18,38)(19,39)(20,40)(21,41)(22,42);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s1*s2*s1*s2*s3*s1*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(47)!(1,2);
s1 := Sym(47)!( 4, 7)( 5, 6)( 8,38)( 9,42)(10,41)(11,40)(12,39)(13,28)(14,32)(15,31)(16,30)(17,29)(18,33)(19,37)(20,36)(21,35)(22,34)(24,27)(25,26)(44,47)(45,46);
s2 := Sym(47)!( 3, 4)( 5, 7)( 8, 9)(10,12)(13,14)(15,17)(18,44)(19,43)(20,47)(21,46)(22,45)(23,34)(24,33)(25,37)(26,36)(27,35)(28,39)(29,38)(30,42)(31,41)(32,40);
s3 := Sym(47)!( 3,23)( 4,24)( 5,25)( 6,26)( 7,27)( 8,33)( 9,34)(10,35)(11,36)(12,37)(18,38)(19,39)(20,40)(21,41)(22,42);
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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s1*s2*s1*s2*s3*s1*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s2*s1 >;