Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1512,838)
Rank
5
Schläfli Type
{3,2,21,6}
Vertices, edges, …
3, 3, 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 := (2,3);;
s1 := (1,2);;
s2 := ( 5,10)( 6, 9)( 7, 8)(11,18)(12,24)(13,23)(14,22)(15,21)(16,20)(17,19)(25,46)(26,52)(27,51)(28,50)(29,49)(30,48)(31,47)(32,60)(33,66)(34,65)(35,64)(36,63)(37,62)(38,61)(39,53)(40,59)(41,58)(42,57)(43,56)(44,55)(45,54);;
s3 := ( 4,33)( 5,32)( 6,38)( 7,37)( 8,36)( 9,35)(10,34)(11,26)(12,25)(13,31)(14,30)(15,29)(16,28)(17,27)(18,40)(19,39)(20,45)(21,44)(22,43)(23,42)(24,41)(46,54)(47,53)(48,59)(49,58)(50,57)(51,56)(52,55)(60,61)(62,66)(63,65);;
s4 := (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)(45,66);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s0*s1*s0*s1, 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(66)!(2,3);
s1 := Sym(66)!(1,2);
s2 := Sym(66)!( 5,10)( 6, 9)( 7, 8)(11,18)(12,24)(13,23)(14,22)(15,21)(16,20)(17,19)(25,46)(26,52)(27,51)(28,50)(29,49)(30,48)(31,47)(32,60)(33,66)(34,65)(35,64)(36,63)(37,62)(38,61)(39,53)(40,59)(41,58)(42,57)(43,56)(44,55)(45,54);
s3 := Sym(66)!( 4,33)( 5,32)( 6,38)( 7,37)( 8,36)( 9,35)(10,34)(11,26)(12,25)(13,31)(14,30)(15,29)(16,28)(17,27)(18,40)(19,39)(20,45)(21,44)(22,43)(23,42)(24,41)(46,54)(47,53)(48,59)(49,58)(50,57)(51,56)(52,55)(60,61)(62,66)(63,65);
s4 := Sym(66)!(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)(45,66);
poly := sub<Sym(66)|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, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, 
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 >;