Part of the Atlas of Small Regular Polytopes

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

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

Overview

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