Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,6,30}

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

Overview

Group
SmallGroup(1080,337)
Rank
4
Schläfli Type
{2,6,30}
Vertices, edges, …
2, 9, 135, 45
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 := (1,2);;
s1 := ( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)(34,35)(37,38)(40,41)(43,44)(46,47);;
s2 := ( 6,15)( 7,16)( 8,17)( 9,12)(10,13)(11,14)(18,35)(19,33)(20,34)(21,47)(22,45)(23,46)(24,44)(25,42)(26,43)(27,41)(28,39)(29,40)(30,38)(31,36)(32,37);;
s3 := ( 3,21)( 4,23)( 5,22)( 6,18)( 7,20)( 8,19)( 9,30)(10,32)(11,31)(12,27)(13,29)(14,28)(15,24)(16,26)(17,25)(33,36)(34,38)(35,37)(39,45)(40,47)(41,46)(43,44);;
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*s1*s2, 
s1*s2*s3*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(47)!(1,2);
s1 := Sym(47)!( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)(34,35)(37,38)(40,41)(43,44)(46,47);
s2 := Sym(47)!( 6,15)( 7,16)( 8,17)( 9,12)(10,13)(11,14)(18,35)(19,33)(20,34)(21,47)(22,45)(23,46)(24,44)(25,42)(26,43)(27,41)(28,39)(29,40)(30,38)(31,36)(32,37);
s3 := Sym(47)!( 3,21)( 4,23)( 5,22)( 6,18)( 7,20)( 8,19)( 9,30)(10,32)(11,31)(12,27)(13,29)(14,28)(15,24)(16,26)(17,25)(33,36)(34,38)(35,37)(39,45)(40,47)(41,46)(43,44);
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*s1*s2, 
s1*s2*s3*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;