Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,4,30}

Atlas Canonical Name {2,4,30}*1440

Overview

Group
SmallGroup(1440,5890)
Rank
4
Schläfli Type
{2,4,30}
Vertices, edges, …
2, 12, 180, 90
Order of s0s1s2s3
20
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

5-fold

9-fold

10-fold

18-fold

36-fold

45-fold

90-fold

Covers minimal covers in bold

None in this atlas.

Representations

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