Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,10,4}

Atlas Canonical Name {3,10,4}*1920a

Overview

Group
SmallGroup(1920,240997)
Rank
4
Schläfli Type
{3,10,4}
Vertices, edges, …
6, 120, 160, 16
Order of s0s1s2s3
10
Order of s0s1s2s3s2s1
4
Also known as
if this polytope has a name.

Special Properties

  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<(s2*s3)^2> of order 2

8 facets

6 vertex figures

Representations

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

References

None.

to this polytope.