Part of the Atlas of Small Regular Polytopes

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

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

Overview

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