Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,2,40}

Atlas Canonical Name {2,2,40}*320

Overview

Group
SmallGroup(320,1412)
Rank
4
Schläfli Type
{2,2,40}
Vertices, edges, …
2, 2, 40, 40
Order of s0s1s2s3
40
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

5-fold

8-fold

10-fold

20-fold

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-fold

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 7)( 8, 9)(10,13)(11,15)(12,14)(16,17)(18,23)(19,25)(20,24)(21,27)(22,26)(29,34)(30,33)(31,36)(32,35)(37,38)(39,42)(40,41)(43,44);;
s3 := ( 5,11)( 6, 8)( 7,19)( 9,21)(10,14)(12,16)(13,29)(15,31)(17,22)(18,24)(20,26)(23,37)(25,39)(27,32)(28,33)(30,35)(34,43)(36,40)(38,41)(42,44);;
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*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*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*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(44)!(1,2);
s1 := Sym(44)!(3,4);
s2 := Sym(44)!( 6, 7)( 8, 9)(10,13)(11,15)(12,14)(16,17)(18,23)(19,25)(20,24)(21,27)(22,26)(29,34)(30,33)(31,36)(32,35)(37,38)(39,42)(40,41)(43,44);
s3 := Sym(44)!( 5,11)( 6, 8)( 7,19)( 9,21)(10,14)(12,16)(13,29)(15,31)(17,22)(18,24)(20,26)(23,37)(25,39)(27,32)(28,33)(30,35)(34,43)(36,40)(38,41)(42,44);
poly := sub<Sym(44)|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*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*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*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 >;