Part of the Atlas of Small Regular Polytopes

Polytope of Type {8,6,2}

Atlas Canonical Name {8,6,2}*960a

Overview

Group
SmallGroup(960,10869)
Rank
4
Schläfli Type
{8,6,2}
Vertices, edges, …
40, 120, 30, 2
Order of s0s1s2s3
10
Order of s0s1s2s3s2s1
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

2-fold

Representations

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