Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1664,19301)
Rank
6
Schläfli Type
{4,26,2,2,2}
Vertices, edges, …
4, 52, 26, 2, 2, 2
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 := (27,40)(28,41)(29,42)(30,43)(31,44)(32,45)(33,46)(34,47)(35,48)(36,49)(37,50)(38,51)(39,52);;
s1 := ( 1,27)( 2,39)( 3,38)( 4,37)( 5,36)( 6,35)( 7,34)( 8,33)( 9,32)(10,31)(11,30)(12,29)(13,28)(14,40)(15,52)(16,51)(17,50)(18,49)(19,48)(20,47)(21,46)(22,45)(23,44)(24,43)(25,42)(26,41);;
s2 := ( 1, 2)( 3,13)( 4,12)( 5,11)( 6,10)( 7, 9)(14,15)(16,26)(17,25)(18,24)(19,23)(20,22)(27,28)(29,39)(30,38)(31,37)(32,36)(33,35)(40,41)(42,52)(43,51)(44,50)(45,49)(46,48);;
s3 := (53,54);;
s4 := (55,56);;
s5 := (57,58);;
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*s2*s0*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, s3*s4*s3*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(58)!(27,40)(28,41)(29,42)(30,43)(31,44)(32,45)(33,46)(34,47)(35,48)(36,49)(37,50)(38,51)(39,52);
s1 := Sym(58)!( 1,27)( 2,39)( 3,38)( 4,37)( 5,36)( 6,35)( 7,34)( 8,33)( 9,32)(10,31)(11,30)(12,29)(13,28)(14,40)(15,52)(16,51)(17,50)(18,49)(19,48)(20,47)(21,46)(22,45)(23,44)(24,43)(25,42)(26,41);
s2 := Sym(58)!( 1, 2)( 3,13)( 4,12)( 5,11)( 6,10)( 7, 9)(14,15)(16,26)(17,25)(18,24)(19,23)(20,22)(27,28)(29,39)(30,38)(31,37)(32,36)(33,35)(40,41)(42,52)(43,51)(44,50)(45,49)(46,48);
s3 := Sym(58)!(53,54);
s4 := Sym(58)!(55,56);
s5 := Sym(58)!(57,58);
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*s2*s0*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, s3*s4*s3*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;