Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,10,10}

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

Overview

Group
SmallGroup(1920,240595)
Rank
4
Schläfli Type
{4,10,10}
Vertices, edges, …
4, 48, 120, 24
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

16-fold

60-fold

120-fold

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)
s0 := ( 1, 6)( 2,14)( 3, 5)( 4,15)( 7,11)( 8,12)( 9,13)(10,16);;
s1 := ( 1,15)( 2, 9)( 3,13)( 4, 8)( 5,11)( 6,10)( 7,14)(12,16)(18,21)(19,20);;
s2 := ( 1, 7)( 2, 4)( 3,16)( 5,10)( 6,11)( 8, 9)(12,13)(14,15)(17,21)(18,20);;
s3 := ( 1,16)( 2, 9)( 3, 7)( 4, 8)( 5,11)( 6,10)(12,15)(13,14)(18,19)(20,21);;
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*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2, 
s1*s2*s1*s2*s3*s2*s3*s2*s1*s2*s1*s2*s3*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(21)!( 1, 6)( 2,14)( 3, 5)( 4,15)( 7,11)( 8,12)( 9,13)(10,16);
s1 := Sym(21)!( 1,15)( 2, 9)( 3,13)( 4, 8)( 5,11)( 6,10)( 7,14)(12,16)(18,21)(19,20);
s2 := Sym(21)!( 1, 7)( 2, 4)( 3,16)( 5,10)( 6,11)( 8, 9)(12,13)(14,15)(17,21)(18,20);
s3 := Sym(21)!( 1,16)( 2, 9)( 3, 7)( 4, 8)( 5,11)( 6,10)(12,15)(13,14)(18,19)(20,21);
poly := sub<Sym(21)|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*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s3*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2, 
s1*s2*s1*s2*s3*s2*s3*s2*s1*s2*s1*s2*s3*s2*s3*s2 >; 

References

None.

to this polytope.