Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,8,4}

Atlas Canonical Name {2,8,4}*256b

Overview

Group
SmallGroup(256,26531)
Rank
4
Schläfli Type
{2,8,4}
Vertices, edges, …
2, 16, 32, 8
Order of s0s1s2s3
4
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

8-fold

16-fold

Covers minimal covers in bold

2-fold

3-fold

5-fold

7-fold

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := ( 3,11)( 4,12)( 5,13)( 6,14)( 7,17)( 8,18)( 9,15)(10,16);;
s2 := ( 5, 6)( 9,10)(11,15)(12,16)(13,18)(14,17);;
s3 := ( 7, 9)( 8,10)(15,17)(16,18);;
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, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
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 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(18)!(1,2);
s1 := Sym(18)!( 3,11)( 4,12)( 5,13)( 6,14)( 7,17)( 8,18)( 9,15)(10,16);
s2 := Sym(18)!( 5, 6)( 9,10)(11,15)(12,16)(13,18)(14,17);
s3 := Sym(18)!( 7, 9)( 8,10)(15,17)(16,18);
poly := sub<Sym(18)|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, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
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 >;