Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,2,4,14}

Atlas Canonical Name {3,2,4,14}*672

Overview

Group
SmallGroup(672,1150)
Rank
5
Schläfli Type
{3,2,4,14}
Vertices, edges, …
3, 3, 4, 28, 14
Order of s0s1s2s3s4
84
Order of s0s1s2s3s4s3s2s1
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

Representations

Permutation Representation (GAP) 
s0 := (2,3);;
s1 := (1,2);;
s2 := ( 5, 8)( 9,14)(10,15)(16,22)(17,23)(24,28)(25,29);;
s3 := ( 4, 5)( 6,10)( 7, 9)( 8,13)(11,17)(12,16)(14,21)(15,20)(18,25)(19,24)(22,27)(23,26)(28,31)(29,30);;
s4 := ( 4, 6)( 5, 9)( 7,11)( 8,14)(10,16)(12,18)(13,20)(15,22)(17,24)(21,26)(23,28)(27,30);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(31)!(2,3);
s1 := Sym(31)!(1,2);
s2 := Sym(31)!( 5, 8)( 9,14)(10,15)(16,22)(17,23)(24,28)(25,29);
s3 := Sym(31)!( 4, 5)( 6,10)( 7, 9)( 8,13)(11,17)(12,16)(14,21)(15,20)(18,25)(19,24)(22,27)(23,26)(28,31)(29,30);
s4 := Sym(31)!( 4, 6)( 5, 9)( 7,11)( 8,14)(10,16)(12,18)(13,20)(15,22)(17,24)(21,26)(23,28)(27,30);
poly := sub<Sym(31)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;