Part of the Atlas of Small Regular Polytopes

Polytope of Type {5,8,2}

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

Overview

Group
SmallGroup(960,10869)
Rank
4
Schläfli Type
{5,8,2}
Vertices, edges, …
30, 120, 48, 2
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 := ( 3,17)( 4,13)( 7,16)( 8,15)( 9,26)(10,14)(11,39)(12,28)(18,33)(19,34)(20,30)(21,37)(22,38)(23,29)(24,40)(25,27)(31,36)(32,35);;
s1 := ( 1, 3)( 2, 9)( 4, 5)( 6,10)( 7,24)( 8,25)(11,15)(12,16)(13,21)(14,20)(17,22)(18,36)(19,35)(23,26)(27,31)(28,34)(32,40)(33,39);;
s2 := ( 2, 5)( 3, 4)( 7,15)( 8,16)( 9,10)(11,22)(12,21)(13,17)(14,26)(18,31)(19,34)(20,25)(23,24)(27,30)(28,37)(29,40)(32,35)(33,36)(38,39);;
s3 := (41,42);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(42)!( 3,17)( 4,13)( 7,16)( 8,15)( 9,26)(10,14)(11,39)(12,28)(18,33)(19,34)(20,30)(21,37)(22,38)(23,29)(24,40)(25,27)(31,36)(32,35);
s1 := Sym(42)!( 1, 3)( 2, 9)( 4, 5)( 6,10)( 7,24)( 8,25)(11,15)(12,16)(13,21)(14,20)(17,22)(18,36)(19,35)(23,26)(27,31)(28,34)(32,40)(33,39);
s2 := Sym(42)!( 2, 5)( 3, 4)( 7,15)( 8,16)( 9,10)(11,22)(12,21)(13,17)(14,26)(18,31)(19,34)(20,25)(23,24)(27,30)(28,37)(29,40)(32,35)(33,36)(38,39);
s3 := Sym(42)!(41,42);
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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;