Part of the Atlas of Small Regular Polytopes

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

Atlas Canonical Name {2,21,6,2}*1008

Overview

Group
SmallGroup(1008,942)
Rank
5
Schläfli Type
{2,21,6,2}
Vertices, edges, …
2, 21, 63, 6, 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 := (1,2);;
s1 := ( 4, 9)( 5, 8)( 6, 7)(10,17)(11,23)(12,22)(13,21)(14,20)(15,19)(16,18)(24,45)(25,51)(26,50)(27,49)(28,48)(29,47)(30,46)(31,59)(32,65)(33,64)(34,63)(35,62)(36,61)(37,60)(38,52)(39,58)(40,57)(41,56)(42,55)(43,54)(44,53);;
s2 := ( 3,32)( 4,31)( 5,37)( 6,36)( 7,35)( 8,34)( 9,33)(10,25)(11,24)(12,30)(13,29)(14,28)(15,27)(16,26)(17,39)(18,38)(19,44)(20,43)(21,42)(22,41)(23,40)(45,53)(46,52)(47,58)(48,57)(49,56)(50,55)(51,54)(59,60)(61,65)(62,64);;
s3 := (24,45)(25,46)(26,47)(27,48)(28,49)(29,50)(30,51)(31,52)(32,53)(33,54)(34,55)(35,56)(36,57)(37,58)(38,59)(39,60)(40,61)(41,62)(42,63)(43,64)(44,65);;
s4 := (66,67);;
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, 
s3*s4*s3*s4, 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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(67)!(1,2);
s1 := Sym(67)!( 4, 9)( 5, 8)( 6, 7)(10,17)(11,23)(12,22)(13,21)(14,20)(15,19)(16,18)(24,45)(25,51)(26,50)(27,49)(28,48)(29,47)(30,46)(31,59)(32,65)(33,64)(34,63)(35,62)(36,61)(37,60)(38,52)(39,58)(40,57)(41,56)(42,55)(43,54)(44,53);
s2 := Sym(67)!( 3,32)( 4,31)( 5,37)( 6,36)( 7,35)( 8,34)( 9,33)(10,25)(11,24)(12,30)(13,29)(14,28)(15,27)(16,26)(17,39)(18,38)(19,44)(20,43)(21,42)(22,41)(23,40)(45,53)(46,52)(47,58)(48,57)(49,56)(50,55)(51,54)(59,60)(61,65)(62,64);
s3 := Sym(67)!(24,45)(25,46)(26,47)(27,48)(28,49)(29,50)(30,51)(31,52)(32,53)(33,54)(34,55)(35,56)(36,57)(37,58)(38,59)(39,60)(40,61)(41,62)(42,63)(43,64)(44,65);
s4 := Sym(67)!(66,67);
poly := sub<Sym(67)|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, s3*s4*s3*s4, 
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;