Part of the Atlas of Small Regular Polytopes

Polytope of Type {7,2,24}

Atlas Canonical Name {7,2,24}*672

Overview

Group
SmallGroup(672,392)
Rank
4
Schläfli Type
{7,2,24}
Vertices, edges, …
7, 7, 24, 24
Order of s0s1s2s3
168
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

3-fold

4-fold

6-fold

8-fold

12-fold

Covers minimal covers in bold

2-fold

Representations

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