Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,2,10,4,2}

Atlas Canonical Name {4,2,10,4,2}*1280

Overview

Group
SmallGroup(1280,1076474)
Rank
6
Schläfli Type
{4,2,10,4,2}
Vertices, edges, …
4, 4, 10, 20, 4, 2
Order of s0s1s2s3s4s5
20
Order of s0s1s2s3s4s5s4s3s2s1
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

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := ( 7, 8)(10,11)(12,13)(15,16)(17,18)(19,20)(21,22)(23,24);;
s3 := ( 5, 7)( 6,15)( 8,12)( 9,10)(11,21)(14,19)(16,17)(18,22)(20,23);;
s4 := ( 5, 6)( 7,10)( 8,11)( 9,14)(12,17)(13,18)(15,19)(16,20)(21,23)(22,24);;
s5 := (25,26);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
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*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5, 
s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, 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(26)!(2,3);
s1 := Sym(26)!(1,2)(3,4);
s2 := Sym(26)!( 7, 8)(10,11)(12,13)(15,16)(17,18)(19,20)(21,22)(23,24);
s3 := Sym(26)!( 5, 7)( 6,15)( 8,12)( 9,10)(11,21)(14,19)(16,17)(18,22)(20,23);
s4 := Sym(26)!( 5, 6)( 7,10)( 8,11)( 9,14)(12,17)(13,18)(15,19)(16,20)(21,23)(22,24);
s5 := Sym(26)!(25,26);
poly := sub<Sym(26)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, 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*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5, s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;