Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,2,4,26}

Atlas Canonical Name {3,2,4,26}*1248

Overview

Group
SmallGroup(1248,1329)
Rank
5
Schläfli Type
{3,2,4,26}
Vertices, edges, …
3, 3, 4, 52, 26
Order of s0s1s2s3s4
156
Order of s0s1s2s3s4s3s2s1
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 := (2,3);;
s1 := (1,2);;
s2 := (30,43)(31,44)(32,45)(33,46)(34,47)(35,48)(36,49)(37,50)(38,51)(39,52)(40,53)(41,54)(42,55);;
s3 := ( 4,30)( 5,42)( 6,41)( 7,40)( 8,39)( 9,38)(10,37)(11,36)(12,35)(13,34)(14,33)(15,32)(16,31)(17,43)(18,55)(19,54)(20,53)(21,52)(22,51)(23,50)(24,49)(25,48)(26,47)(27,46)(28,45)(29,44);;
s4 := ( 4, 5)( 6,16)( 7,15)( 8,14)( 9,13)(10,12)(17,18)(19,29)(20,28)(21,27)(22,26)(23,25)(30,31)(32,42)(33,41)(34,40)(35,39)(36,38)(43,44)(45,55)(46,54)(47,53)(48,52)(49,51);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, 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(55)!(2,3);
s1 := Sym(55)!(1,2);
s2 := Sym(55)!(30,43)(31,44)(32,45)(33,46)(34,47)(35,48)(36,49)(37,50)(38,51)(39,52)(40,53)(41,54)(42,55);
s3 := Sym(55)!( 4,30)( 5,42)( 6,41)( 7,40)( 8,39)( 9,38)(10,37)(11,36)(12,35)(13,34)(14,33)(15,32)(16,31)(17,43)(18,55)(19,54)(20,53)(21,52)(22,51)(23,50)(24,49)(25,48)(26,47)(27,46)(28,45)(29,44);
s4 := Sym(55)!( 4, 5)( 6,16)( 7,15)( 8,14)( 9,13)(10,12)(17,18)(19,29)(20,28)(21,27)(22,26)(23,25)(30,31)(32,42)(33,41)(34,40)(35,39)(36,38)(43,44)(45,55)(46,54)(47,53)(48,52)(49,51);
poly := sub<Sym(55)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
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 >;