Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,2,4}

Atlas Canonical Name {3,2,4}*48

Overview

Group
SmallGroup(48,38)
Rank
4
Schläfli Type
{3,2,4}
Vertices, edges, …
3, 3, 4, 4
Order of s0s1s2s3
12
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Projective
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

Covers minimal covers in bold

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Representations

Permutation Representation (GAP) 
s0 := (2,3);;
s1 := (1,2);;
s2 := (5,6);;
s3 := (4,5)(6,7);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(7)!(2,3);
s1 := Sym(7)!(1,2);
s2 := Sym(7)!(5,6);
s3 := Sym(7)!(4,5)(6,7);
poly := sub<Sym(7)|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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3 >;