Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,6,21,2}

Atlas Canonical Name {3,6,21,2}*1512

Overview

Group
SmallGroup(1512,561)
Rank
5
Schläfli Type
{3,6,21,2}
Vertices, edges, …
3, 9, 63, 21, 2
Order of s0s1s2s3s4
42
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

7-fold

9-fold

21-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := ( 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)(47,48)(50,51)(53,54)(56,57)(59,60)(62,63);;
s1 := ( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(22,23)(25,26)(28,29)(31,32)(34,35)(37,38)(40,41)(43,45)(46,48)(49,51)(52,54)(55,57)(58,60)(61,63);;
s2 := ( 1,22)( 2,24)( 3,23)( 4,40)( 5,42)( 6,41)( 7,37)( 8,39)( 9,38)(10,34)(11,36)(12,35)(13,31)(14,33)(15,32)(16,28)(17,30)(18,29)(19,25)(20,27)(21,26)(44,45)(46,61)(47,63)(48,62)(49,58)(50,60)(51,59)(52,55)(53,57)(54,56);;
s3 := ( 1, 4)( 2, 6)( 3, 5)( 7,19)( 8,21)( 9,20)(10,16)(11,18)(12,17)(14,15)(22,46)(23,48)(24,47)(25,43)(26,45)(27,44)(28,61)(29,63)(30,62)(31,58)(32,60)(33,59)(34,55)(35,57)(36,56)(37,52)(38,54)(39,53)(40,49)(41,51)(42,50);;
s4 := (64,65);;
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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(65)!( 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)(47,48)(50,51)(53,54)(56,57)(59,60)(62,63);
s1 := Sym(65)!( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(22,23)(25,26)(28,29)(31,32)(34,35)(37,38)(40,41)(43,45)(46,48)(49,51)(52,54)(55,57)(58,60)(61,63);
s2 := Sym(65)!( 1,22)( 2,24)( 3,23)( 4,40)( 5,42)( 6,41)( 7,37)( 8,39)( 9,38)(10,34)(11,36)(12,35)(13,31)(14,33)(15,32)(16,28)(17,30)(18,29)(19,25)(20,27)(21,26)(44,45)(46,61)(47,63)(48,62)(49,58)(50,60)(51,59)(52,55)(53,57)(54,56);
s3 := Sym(65)!( 1, 4)( 2, 6)( 3, 5)( 7,19)( 8,21)( 9,20)(10,16)(11,18)(12,17)(14,15)(22,46)(23,48)(24,47)(25,43)(26,45)(27,44)(28,61)(29,63)(30,62)(31,58)(32,60)(33,59)(34,55)(35,57)(36,56)(37,52)(38,54)(39,53)(40,49)(41,51)(42,50);
s4 := Sym(65)!(64,65);
poly := sub<Sym(65)|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, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;