Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,2,2,26,4}

Atlas Canonical Name {2,2,2,26,4}*1664

Overview

Group
SmallGroup(1664,19301)
Rank
6
Schläfli Type
{2,2,2,26,4}
Vertices, edges, …
2, 2, 2, 26, 52, 4
Order of s0s1s2s3s4s5
52
Order of s0s1s2s3s4s5s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

4-fold

13-fold

26-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := ( 8,19)( 9,18)(10,17)(11,16)(12,15)(13,14)(21,32)(22,31)(23,30)(24,29)(25,28)(26,27)(34,45)(35,44)(36,43)(37,42)(38,41)(39,40)(47,58)(48,57)(49,56)(50,55)(51,54)(52,53);;
s4 := ( 7, 8)( 9,19)(10,18)(11,17)(12,16)(13,15)(20,21)(22,32)(23,31)(24,30)(25,29)(26,28)(33,47)(34,46)(35,58)(36,57)(37,56)(38,55)(39,54)(40,53)(41,52)(42,51)(43,50)(44,49)(45,48);;
s5 := ( 7,33)( 8,34)( 9,35)(10,36)(11,37)(12,38)(13,39)(14,40)(15,41)(16,42)(17,43)(18,44)(19,45)(20,46)(21,47)(22,48)(23,49)(24,50)(25,51)(26,52)(27,53)(28,54)(29,55)(30,56)(31,57)(32,58);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s3*s4*s5*s4*s3*s4*s5*s4, 
s4*s5*s4*s5*s4*s5*s4*s5, 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*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(58)!(1,2);
s1 := Sym(58)!(3,4);
s2 := Sym(58)!(5,6);
s3 := Sym(58)!( 8,19)( 9,18)(10,17)(11,16)(12,15)(13,14)(21,32)(22,31)(23,30)(24,29)(25,28)(26,27)(34,45)(35,44)(36,43)(37,42)(38,41)(39,40)(47,58)(48,57)(49,56)(50,55)(51,54)(52,53);
s4 := Sym(58)!( 7, 8)( 9,19)(10,18)(11,17)(12,16)(13,15)(20,21)(22,32)(23,31)(24,30)(25,29)(26,28)(33,47)(34,46)(35,58)(36,57)(37,56)(38,55)(39,54)(40,53)(41,52)(42,51)(43,50)(44,49)(45,48);
s5 := Sym(58)!( 7,33)( 8,34)( 9,35)(10,36)(11,37)(12,38)(13,39)(14,40)(15,41)(16,42)(17,43)(18,44)(19,45)(20,46)(21,47)(22,48)(23,49)(24,50)(25,51)(26,52)(27,53)(28,54)(29,55)(30,56)(31,57)(32,58);
poly := sub<Sym(58)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s3*s4*s5*s4*s3*s4*s5*s4, 
s4*s5*s4*s5*s4*s5*s4*s5, 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*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;