Part of the Atlas of Small Regular Polytopes

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

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

Overview

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