Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,2,6,30}

Atlas Canonical Name {2,2,6,30}*1440a

Overview

Group
SmallGroup(1440,5924)
Rank
5
Schläfli Type
{2,2,6,30}
Vertices, edges, …
2, 2, 6, 90, 30
Order of s0s1s2s3s4
30
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

3-fold

5-fold

9-fold

10-fold

15-fold

18-fold

30-fold

45-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP)
s0 := (1,2);;
s1 := (3,4);;
s2 := (10,15)(11,16)(12,17)(13,18)(14,19)(20,35)(21,36)(22,37)(23,38)(24,39)(25,45)(26,46)(27,47)(28,48)(29,49)(30,40)(31,41)(32,42)(33,43)(34,44);;
s3 := ( 5,25)( 6,29)( 7,28)( 8,27)( 9,26)(10,20)(11,24)(12,23)(13,22)(14,21)(15,30)(16,34)(17,33)(18,32)(19,31)(35,40)(36,44)(37,43)(38,42)(39,41)(46,49)(47,48);;
s4 := ( 5, 6)( 7, 9)(10,16)(11,15)(12,19)(13,18)(14,17)(20,21)(22,24)(25,31)(26,30)(27,34)(28,33)(29,32)(35,36)(37,39)(40,46)(41,45)(42,49)(43,48)(44,47);;
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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s4*s2*s3*s2*s3*s4*s3*s4*s2*s3, 
s4*s3*s2*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s2*s4*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(49)!(1,2);
s1 := Sym(49)!(3,4);
s2 := Sym(49)!(10,15)(11,16)(12,17)(13,18)(14,19)(20,35)(21,36)(22,37)(23,38)(24,39)(25,45)(26,46)(27,47)(28,48)(29,49)(30,40)(31,41)(32,42)(33,43)(34,44);
s3 := Sym(49)!( 5,25)( 6,29)( 7,28)( 8,27)( 9,26)(10,20)(11,24)(12,23)(13,22)(14,21)(15,30)(16,34)(17,33)(18,32)(19,31)(35,40)(36,44)(37,43)(38,42)(39,41)(46,49)(47,48);
s4 := Sym(49)!( 5, 6)( 7, 9)(10,16)(11,15)(12,19)(13,18)(14,17)(20,21)(22,24)(25,31)(26,30)(27,34)(28,33)(29,32)(35,36)(37,39)(40,46)(41,45)(42,49)(43,48)(44,47);
poly := sub<Sym(49)|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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s4*s2*s3*s2*s3*s4*s3*s4*s2*s3, 
s4*s3*s2*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s2*s4*s3 >;