Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,14,2}

Atlas Canonical Name {4,14,2}*224

Overview

Group
SmallGroup(224,178)
Rank
4
Schläfli Type
{4,14,2}
Vertices, edges, …
4, 28, 14, 2
Order of s0s1s2s3
28
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

7-fold

14-fold

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-fold

7-fold

8-fold

Representations

Permutation Representation (GAP) 
s0 := ( 2, 5)( 6,11)( 7,12)(13,19)(14,20)(21,25)(22,26);;
s1 := ( 1, 2)( 3, 7)( 4, 6)( 5,10)( 8,14)( 9,13)(11,18)(12,17)(15,22)(16,21)(19,24)(20,23)(25,28)(26,27);;
s2 := ( 1, 3)( 2, 6)( 4, 8)( 5,11)( 7,13)( 9,15)(10,17)(12,19)(14,21)(18,23)(20,25)(24,27);;
s3 := (29,30);;
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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(30)!( 2, 5)( 6,11)( 7,12)(13,19)(14,20)(21,25)(22,26);
s1 := Sym(30)!( 1, 2)( 3, 7)( 4, 6)( 5,10)( 8,14)( 9,13)(11,18)(12,17)(15,22)(16,21)(19,24)(20,23)(25,28)(26,27);
s2 := Sym(30)!( 1, 3)( 2, 6)( 4, 8)( 5,11)( 7,13)( 9,15)(10,17)(12,19)(14,21)(18,23)(20,25)(24,27);
s3 := Sym(30)!(29,30);
poly := sub<Sym(30)|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*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;