Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,20,6}

Atlas Canonical Name {2,20,6}*720

Overview

Group
SmallGroup(720,810)
Rank
4
Schläfli Type
{2,20,6}
Vertices, edges, …
2, 30, 90, 9
Order of s0s1s2s3
20
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

5-fold

Covers minimal covers in bold

2-fold

Representations

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