Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,3,6,15}

Atlas Canonical Name {2,3,6,15}*1080

Overview

Group
SmallGroup(1080,337)
Rank
5
Schläfli Type
{2,3,6,15}
Vertices, edges, …
2, 3, 9, 45, 15
Order of s0s1s2s3s4
30
Order of s0s1s2s3s4s3s2s1
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

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 := ( 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);;
s3 := ( 3,18)( 4,20)( 5,19)( 6,30)( 7,32)( 8,31)( 9,27)(10,29)(11,28)(12,24)(13,26)(14,25)(15,21)(16,23)(17,22)(34,35)(36,45)(37,47)(38,46)(39,42)(40,44)(41,43);;
s4 := ( 3, 6)( 4, 8)( 5, 7)( 9,15)(10,17)(11,16)(13,14)(18,36)(19,38)(20,37)(21,33)(22,35)(23,34)(24,45)(25,47)(26,46)(27,42)(28,44)(29,43)(30,39)(31,41)(32,40);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s2*s3*s4*s2*s3*s2*s3*s4*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
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)!( 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);
s3 := Sym(47)!( 3,18)( 4,20)( 5,19)( 6,30)( 7,32)( 8,31)( 9,27)(10,29)(11,28)(12,24)(13,26)(14,25)(15,21)(16,23)(17,22)(34,35)(36,45)(37,47)(38,46)(39,42)(40,44)(41,43);
s4 := Sym(47)!( 3, 6)( 4, 8)( 5, 7)( 9,15)(10,17)(11,16)(13,14)(18,36)(19,38)(20,37)(21,33)(22,35)(23,34)(24,45)(25,47)(26,46)(27,42)(28,44)(29,43)(30,39)(31,41)(32,40);
poly := sub<Sym(47)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s2*s3*s4*s2*s3*s2*s3*s4*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;