Part of the Atlas of Small Regular Polytopes

Polytope of Type {28,6,2}

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

Overview

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