Part of the Atlas of Small Regular Polytopes

Polytope of Type {15,6,2}

Atlas Canonical Name {15,6,2}*1080

Overview

Group
SmallGroup(1080,337)
Rank
4
Schläfli Type
{15,6,2}
Vertices, edges, …
45, 135, 18, 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

15-fold

27-fold

45-fold

Covers minimal covers in bold

None in this atlas.

Representations

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