Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,8,5}

Atlas Canonical Name {2,8,5}*960

Overview

Group
SmallGroup(960,10869)
Rank
4
Schläfli Type
{2,8,5}
Vertices, edges, …
2, 48, 120, 30
Order of s0s1s2s3
6
Order of s0s1s2s3s2s1
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

2-fold

Representations

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