Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,2,6,10}

Atlas Canonical Name {2,2,6,10}*1200

Overview

Group
SmallGroup(1200,980)
Rank
5
Schläfli Type
{2,2,6,10}
Vertices, edges, …
2, 2, 15, 75, 25
Order of s0s1s2s3s4
6
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

No regular quotients.

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := (3,4);;
s2 := (10,27)(11,28)(12,29)(13,25)(14,26)(15,24)(16,20)(17,21)(18,22)(19,23);;
s3 := ( 6,12)( 7,19)( 8,21)( 9,28)(10,22)(11,29)(14,15)(17,23)(18,25)(20,26);;
s4 := ( 5, 6)( 7, 9)(10,26)(11,25)(12,29)(13,28)(14,27)(15,21)(16,20)(17,24)(18,23)(19,22);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
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, s2*s3*s4*s2*s3*s4*s2*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(29)!(1,2);
s1 := Sym(29)!(3,4);
s2 := Sym(29)!(10,27)(11,28)(12,29)(13,25)(14,26)(15,24)(16,20)(17,21)(18,22)(19,23);
s3 := Sym(29)!( 6,12)( 7,19)( 8,21)( 9,28)(10,22)(11,29)(14,15)(17,23)(18,25)(20,26);
s4 := Sym(29)!( 5, 6)( 7, 9)(10,26)(11,25)(12,29)(13,28)(14,27)(15,21)(16,20)(17,24)(18,23)(19,22);
poly := sub<Sym(29)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, 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, 
s2*s3*s4*s2*s3*s4*s2*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;