Part of the Atlas of Small Regular Polytopes

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

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

Overview

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