Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,30,2}

Atlas Canonical Name {6,30,2}*1080

Overview

Group
SmallGroup(1080,337)
Rank
4
Schläfli Type
{6,30,2}
Vertices, edges, …
9, 135, 45, 2
Order of s0s1s2s3
30
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

5-fold

Covers minimal covers in bold

None in this atlas.

Representations

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