Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1440,5921)
Rank
5
Schläfli Type
{6,20,2,2}
Vertices, edges, …
9, 90, 30, 2, 2
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 := ( 6,11)( 7,12)( 8,13)( 9,14)(10,15)(16,31)(17,32)(18,33)(19,34)(20,35)(21,41)(22,42)(23,43)(24,44)(25,45)(26,36)(27,37)(28,38)(29,39)(30,40);;
s1 := ( 1, 6)( 2,10)( 3, 9)( 4, 8)( 5, 7)(12,15)(13,14)(16,21)(17,25)(18,24)(19,23)(20,22)(27,30)(28,29)(31,36)(32,40)(33,39)(34,38)(35,37)(42,45)(43,44);;
s2 := ( 1, 2)( 3, 5)( 6,17)( 7,16)( 8,20)( 9,19)(10,18)(11,32)(12,31)(13,35)(14,34)(15,33)(21,22)(23,25)(26,37)(27,36)(28,40)(29,39)(30,38)(41,42)(43,45);;
s3 := (46,47);;
s4 := (48,49);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1, 
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(49)!( 6,11)( 7,12)( 8,13)( 9,14)(10,15)(16,31)(17,32)(18,33)(19,34)(20,35)(21,41)(22,42)(23,43)(24,44)(25,45)(26,36)(27,37)(28,38)(29,39)(30,40);
s1 := Sym(49)!( 1, 6)( 2,10)( 3, 9)( 4, 8)( 5, 7)(12,15)(13,14)(16,21)(17,25)(18,24)(19,23)(20,22)(27,30)(28,29)(31,36)(32,40)(33,39)(34,38)(35,37)(42,45)(43,44);
s2 := Sym(49)!( 1, 2)( 3, 5)( 6,17)( 7,16)( 8,20)( 9,19)(10,18)(11,32)(12,31)(13,35)(14,34)(15,33)(21,22)(23,25)(26,37)(27,36)(28,40)(29,39)(30,38)(41,42)(43,45);
s3 := Sym(49)!(46,47);
s4 := Sym(49)!(48,49);
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*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1, 
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;