Part of the Atlas of Small Regular Polytopes

Polytope of Type {30,6,2}

Atlas Canonical Name {30,6,2}*720a

Overview

Group
SmallGroup(720,813)
Rank
4
Schläfli Type
{30,6,2}
Vertices, edges, …
30, 90, 6, 2
Order of s0s1s2s3
30
Order of s0s1s2s3s2s1
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

2-fold

Representations

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