Part of the Atlas of Small Regular Polytopes

Polytope of Type {30,6,2}

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

Overview

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