Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,2,21,6}

Atlas Canonical Name {2,2,21,6}*1344

Overview

Group
SmallGroup(1344,11695)
Rank
5
Schläfli Type
{2,2,21,6}
Vertices, edges, …
2, 2, 28, 84, 8
Order of s0s1s2s3s4
28
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

7-fold

12-fold

14-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 7)( 9,29)(10,31)(11,30)(12,32)(13,25)(14,27)(15,26)(16,28)(17,21)(18,23)(19,22)(20,24);;
s3 := ( 5, 9)( 6,10)( 7,12)( 8,11)(13,29)(14,30)(15,32)(16,31)(17,25)(18,26)(19,28)(20,27)(23,24);;
s4 := ( 5, 8)( 9,12)(13,16)(17,20)(21,24)(25,28)(29,32);;
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*s1*s0*s1, 
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, s2*s3*s2*s3*s4*s3*s2*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s2*s3*s4*s2*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(32)!(1,2);
s1 := Sym(32)!(3,4);
s2 := Sym(32)!( 6, 7)( 9,29)(10,31)(11,30)(12,32)(13,25)(14,27)(15,26)(16,28)(17,21)(18,23)(19,22)(20,24);
s3 := Sym(32)!( 5, 9)( 6,10)( 7,12)( 8,11)(13,29)(14,30)(15,32)(16,31)(17,25)(18,26)(19,28)(20,27)(23,24);
s4 := Sym(32)!( 5, 8)( 9,12)(13,16)(17,20)(21,24)(25,28)(29,32);
poly := sub<Sym(32)|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*s1*s0*s1, 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, 
s2*s3*s2*s3*s4*s3*s2*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s2*s3*s4*s2*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3*s2*s3*s2 >;