Part of the Atlas of Small Regular Polytopes

Polytope of Type {5,10,4}

Atlas Canonical Name {5,10,4}*960

Overview

Group
SmallGroup(960,10886)
Rank
4
Schläfli Type
{5,10,4}
Vertices, edges, …
12, 60, 48, 4
Order of s0s1s2s3
12
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

Covers minimal covers in bold

2-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)
s0 := ( 1, 2)( 8, 9)(10,11);;
s1 := ( 1, 2)( 7, 8)( 9,10);;
s2 := ( 4, 6)( 8,10)( 9,11);;
s3 := (3,4)(5,6);;
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, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(11)!( 1, 2)( 8, 9)(10,11);
s1 := Sym(11)!( 1, 2)( 7, 8)( 9,10);
s2 := Sym(11)!( 4, 6)( 8,10)( 9,11);
s3 := Sym(11)!(3,4)(5,6);
poly := sub<Sym(11)|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, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1 >; 

References

None.

to this polytope.