Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,28,6}

Atlas Canonical Name {2,28,6}*1008

Overview

Group
SmallGroup(1008,919)
Rank
4
Schläfli Type
{2,28,6}
Vertices, edges, …
2, 42, 126, 9
Order of s0s1s2s3
28
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

7-fold

Covers minimal covers in bold

None in this atlas.

Representations

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