Part of the Atlas of Small Regular Polytopes

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

Atlas Canonical Name {2,2,2,15,6}*1440

Overview

Group
SmallGroup(1440,5949)
Rank
6
Schläfli Type
{2,2,2,15,6}
Vertices, edges, …
2, 2, 2, 15, 45, 6
Order of s0s1s2s3s4s5
30
Order of s0s1s2s3s4s5s4s3s2s1
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 := (3,4);;
s2 := (5,6);;
s3 := ( 8,11)( 9,10)(12,17)(13,21)(14,20)(15,19)(16,18)(22,37)(23,41)(24,40)(25,39)(26,38)(27,47)(28,51)(29,50)(30,49)(31,48)(32,42)(33,46)(34,45)(35,44)(36,43);;
s4 := ( 7,28)( 8,27)( 9,31)(10,30)(11,29)(12,23)(13,22)(14,26)(15,25)(16,24)(17,33)(18,32)(19,36)(20,35)(21,34)(37,43)(38,42)(39,46)(40,45)(41,44)(47,48)(49,51);;
s5 := (22,37)(23,38)(24,39)(25,40)(26,41)(27,42)(28,43)(29,44)(30,45)(31,46)(32,47)(33,48)(34,49)(35,50)(36,51);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s5*s3*s4*s5*s4*s5*s3*s4*s5*s4, 
s3*s4*s3*s4*s5*s4*s3*s4*s3*s4*s5*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*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(51)!(1,2);
s1 := Sym(51)!(3,4);
s2 := Sym(51)!(5,6);
s3 := Sym(51)!( 8,11)( 9,10)(12,17)(13,21)(14,20)(15,19)(16,18)(22,37)(23,41)(24,40)(25,39)(26,38)(27,47)(28,51)(29,50)(30,49)(31,48)(32,42)(33,46)(34,45)(35,44)(36,43);
s4 := Sym(51)!( 7,28)( 8,27)( 9,31)(10,30)(11,29)(12,23)(13,22)(14,26)(15,25)(16,24)(17,33)(18,32)(19,36)(20,35)(21,34)(37,43)(38,42)(39,46)(40,45)(41,44)(47,48)(49,51);
s5 := Sym(51)!(22,37)(23,38)(24,39)(25,40)(26,41)(27,42)(28,43)(29,44)(30,45)(31,46)(32,47)(33,48)(34,49)(35,50)(36,51);
poly := sub<Sym(51)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s5*s3*s4*s5*s4*s5*s3*s4*s5*s4, 
s3*s4*s3*s4*s5*s4*s3*s4*s3*s4*s5*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*s3*s4 >;