Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,21,2}

Atlas Canonical Name {4,21,2}*336

Overview

Group
SmallGroup(336,215)
Rank
4
Schläfli Type
{4,21,2}
Vertices, edges, …
4, 42, 21, 2
Order of s0s1s2s3
42
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

7-fold

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

Representations

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