Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,30,6}

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

Overview

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