Part of the Atlas of Small Regular Polytopes

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

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

Overview

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