Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,2,5,6}

Atlas Canonical Name {2,2,5,6}*1920

Overview

Group
SmallGroup(1920,240973)
Rank
5
Schläfli Type
{2,2,5,6}
Vertices, edges, …
2, 2, 40, 120, 48
Order of s0s1s2s3s4
8
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

4-fold

Covers minimal covers in bold

None in this atlas.

Representations

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