Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,2,6,8}

Atlas Canonical Name {2,2,6,8}*1920b

Overview

Group
SmallGroup(1920,240973)
Rank
5
Schläfli Type
{2,2,6,8}
Vertices, edges, …
2, 2, 30, 120, 40
Order of s0s1s2s3s4
10
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

2-fold

4-fold

Covers minimal covers in bold

None in this atlas.

Representations

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