Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,28,2}

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

Overview

Group
SmallGroup(1008,919)
Rank
4
Schläfli Type
{6,28,2}
Vertices, edges, …
9, 126, 42, 2
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 := ( 8,15)( 9,16)(10,17)(11,18)(12,19)(13,20)(14,21)(22,43)(23,44)(24,45)(25,46)(26,47)(27,48)(28,49)(29,57)(30,58)(31,59)(32,60)(33,61)(34,62)(35,63)(36,50)(37,51)(38,52)(39,53)(40,54)(41,55)(42,56);;
s1 := ( 1, 8)( 2,14)( 3,13)( 4,12)( 5,11)( 6,10)( 7, 9)(16,21)(17,20)(18,19)(22,29)(23,35)(24,34)(25,33)(26,32)(27,31)(28,30)(37,42)(38,41)(39,40)(43,50)(44,56)(45,55)(46,54)(47,53)(48,52)(49,51)(58,63)(59,62)(60,61);;
s2 := ( 1, 2)( 3, 7)( 4, 6)( 8,23)( 9,22)(10,28)(11,27)(12,26)(13,25)(14,24)(15,44)(16,43)(17,49)(18,48)(19,47)(20,46)(21,45)(29,30)(31,35)(32,34)(36,51)(37,50)(38,56)(39,55)(40,54)(41,53)(42,52)(57,58)(59,63)(60,62);;
s3 := (64,65);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1, 
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*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(65)!( 8,15)( 9,16)(10,17)(11,18)(12,19)(13,20)(14,21)(22,43)(23,44)(24,45)(25,46)(26,47)(27,48)(28,49)(29,57)(30,58)(31,59)(32,60)(33,61)(34,62)(35,63)(36,50)(37,51)(38,52)(39,53)(40,54)(41,55)(42,56);
s1 := Sym(65)!( 1, 8)( 2,14)( 3,13)( 4,12)( 5,11)( 6,10)( 7, 9)(16,21)(17,20)(18,19)(22,29)(23,35)(24,34)(25,33)(26,32)(27,31)(28,30)(37,42)(38,41)(39,40)(43,50)(44,56)(45,55)(46,54)(47,53)(48,52)(49,51)(58,63)(59,62)(60,61);
s2 := Sym(65)!( 1, 2)( 3, 7)( 4, 6)( 8,23)( 9,22)(10,28)(11,27)(12,26)(13,25)(14,24)(15,44)(16,43)(17,49)(18,48)(19,47)(20,46)(21,45)(29,30)(31,35)(32,34)(36,51)(37,50)(38,56)(39,55)(40,54)(41,53)(42,52)(57,58)(59,63)(60,62);
s3 := Sym(65)!(64,65);
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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1, 
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;