Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,2,20,6}

Atlas Canonical Name {2,2,20,6}*1440

Overview

Group
SmallGroup(1440,5921)
Rank
5
Schläfli Type
{2,2,20,6}
Vertices, edges, …
2, 2, 30, 90, 9
Order of s0s1s2s3s4
20
Order of s0s1s2s3s4s3s2s1
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

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 9)( 7, 8)(10,20)(11,24)(12,23)(13,22)(14,21)(15,35)(16,39)(17,38)(18,37)(19,36)(26,29)(27,28)(30,40)(31,44)(32,43)(33,42)(34,41)(46,49)(47,48);;
s3 := ( 5, 6)( 7, 9)(10,16)(11,15)(12,19)(13,18)(14,17)(20,21)(22,24)(25,31)(26,30)(27,34)(28,33)(29,32)(35,36)(37,39)(40,46)(41,45)(42,49)(43,48)(44,47);;
s4 := ( 5,25)( 6,26)( 7,27)( 8,28)( 9,29)(10,20)(11,21)(12,22)(13,23)(14,24)(15,30)(16,31)(17,32)(18,33)(19,34)(35,40)(36,41)(37,42)(38,43)(39,44);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s4*s3*s4*s2*s3*s4*s2*s3*s4*s3*s2*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s4*s3*s2*s3*s2*s4*s3*s2*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(49)!(1,2);
s1 := Sym(49)!(3,4);
s2 := Sym(49)!( 6, 9)( 7, 8)(10,20)(11,24)(12,23)(13,22)(14,21)(15,35)(16,39)(17,38)(18,37)(19,36)(26,29)(27,28)(30,40)(31,44)(32,43)(33,42)(34,41)(46,49)(47,48);
s3 := Sym(49)!( 5, 6)( 7, 9)(10,16)(11,15)(12,19)(13,18)(14,17)(20,21)(22,24)(25,31)(26,30)(27,34)(28,33)(29,32)(35,36)(37,39)(40,46)(41,45)(42,49)(43,48)(44,47);
s4 := Sym(49)!( 5,25)( 6,26)( 7,27)( 8,28)( 9,29)(10,20)(11,21)(12,22)(13,23)(14,24)(15,30)(16,31)(17,32)(18,33)(19,34)(35,40)(36,41)(37,42)(38,43)(39,44);
poly := sub<Sym(49)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s4*s3*s4*s2*s3*s4*s2*s3*s4*s3*s2*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s4*s3*s2*s3*s2*s4*s3*s2*s3*s4 >;