Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,15,6,2}

Atlas Canonical Name {4,15,6,2}*1440

Overview

Group
SmallGroup(1440,5900)
Rank
5
Schläfli Type
{4,15,6,2}
Vertices, edges, …
4, 30, 45, 6, 2
Order of s0s1s2s3s4
30
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

3-fold

5-fold

15-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16)(17,19)(18,20)(21,23)(22,24)(25,27)(26,28)(29,31)(30,32)(33,35)(34,36)(37,39)(38,40)(41,43)(42,44)(45,47)(46,48)(49,51)(50,52)(53,55)(54,56)(57,59)(58,60);;
s1 := ( 2, 3)( 5,17)( 6,19)( 7,18)( 8,20)( 9,13)(10,15)(11,14)(12,16)(21,41)(22,43)(23,42)(24,44)(25,57)(26,59)(27,58)(28,60)(29,53)(30,55)(31,54)(32,56)(33,49)(34,51)(35,50)(36,52)(37,45)(38,47)(39,46)(40,48);;
s2 := ( 1,25)( 2,28)( 3,27)( 4,26)( 5,21)( 6,24)( 7,23)( 8,22)( 9,37)(10,40)(11,39)(12,38)(13,33)(14,36)(15,35)(16,34)(17,29)(18,32)(19,31)(20,30)(41,45)(42,48)(43,47)(44,46)(49,57)(50,60)(51,59)(52,58)(54,56);;
s3 := (21,41)(22,42)(23,43)(24,44)(25,45)(26,46)(27,47)(28,48)(29,49)(30,50)(31,51)(32,52)(33,53)(34,54)(35,55)(36,56)(37,57)(38,58)(39,59)(40,60);;
s4 := (61,62);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s0*s1, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(62)!( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16)(17,19)(18,20)(21,23)(22,24)(25,27)(26,28)(29,31)(30,32)(33,35)(34,36)(37,39)(38,40)(41,43)(42,44)(45,47)(46,48)(49,51)(50,52)(53,55)(54,56)(57,59)(58,60);
s1 := Sym(62)!( 2, 3)( 5,17)( 6,19)( 7,18)( 8,20)( 9,13)(10,15)(11,14)(12,16)(21,41)(22,43)(23,42)(24,44)(25,57)(26,59)(27,58)(28,60)(29,53)(30,55)(31,54)(32,56)(33,49)(34,51)(35,50)(36,52)(37,45)(38,47)(39,46)(40,48);
s2 := Sym(62)!( 1,25)( 2,28)( 3,27)( 4,26)( 5,21)( 6,24)( 7,23)( 8,22)( 9,37)(10,40)(11,39)(12,38)(13,33)(14,36)(15,35)(16,34)(17,29)(18,32)(19,31)(20,30)(41,45)(42,48)(43,47)(44,46)(49,57)(50,60)(51,59)(52,58)(54,56);
s3 := Sym(62)!(21,41)(22,42)(23,43)(24,44)(25,45)(26,46)(27,47)(28,48)(29,49)(30,50)(31,51)(32,52)(33,53)(34,54)(35,55)(36,56)(37,57)(38,58)(39,59)(40,60);
s4 := Sym(62)!(61,62);
poly := sub<Sym(62)|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*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s0*s1, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;