Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,6,26,2}

Atlas Canonical Name {2,6,26,2}*1248

Overview

Group
SmallGroup(1248,1451)
Rank
5
Schläfli Type
{2,6,26,2}
Vertices, edges, …
2, 6, 78, 26, 2
Order of s0s1s2s3s4
78
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

3-fold

6-fold

13-fold

26-fold

39-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP)
s0 := (1,2);;
s1 := (16,29)(17,30)(18,31)(19,32)(20,33)(21,34)(22,35)(23,36)(24,37)(25,38)(26,39)(27,40)(28,41)(55,68)(56,69)(57,70)(58,71)(59,72)(60,73)(61,74)(62,75)(63,76)(64,77)(65,78)(66,79)(67,80);;
s2 := ( 3,16)( 4,28)( 5,27)( 6,26)( 7,25)( 8,24)( 9,23)(10,22)(11,21)(12,20)(13,19)(14,18)(15,17)(30,41)(31,40)(32,39)(33,38)(34,37)(35,36)(42,55)(43,67)(44,66)(45,65)(46,64)(47,63)(48,62)(49,61)(50,60)(51,59)(52,58)(53,57)(54,56)(69,80)(70,79)(71,78)(72,77)(73,76)(74,75);;
s3 := ( 3,43)( 4,42)( 5,54)( 6,53)( 7,52)( 8,51)( 9,50)(10,49)(11,48)(12,47)(13,46)(14,45)(15,44)(16,56)(17,55)(18,67)(19,66)(20,65)(21,64)(22,63)(23,62)(24,61)(25,60)(26,59)(27,58)(28,57)(29,69)(30,68)(31,80)(32,79)(33,78)(34,77)(35,76)(36,75)(37,74)(38,73)(39,72)(40,71)(41,70);;
s4 := (81,82);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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(82)!(1,2);
s1 := Sym(82)!(16,29)(17,30)(18,31)(19,32)(20,33)(21,34)(22,35)(23,36)(24,37)(25,38)(26,39)(27,40)(28,41)(55,68)(56,69)(57,70)(58,71)(59,72)(60,73)(61,74)(62,75)(63,76)(64,77)(65,78)(66,79)(67,80);
s2 := Sym(82)!( 3,16)( 4,28)( 5,27)( 6,26)( 7,25)( 8,24)( 9,23)(10,22)(11,21)(12,20)(13,19)(14,18)(15,17)(30,41)(31,40)(32,39)(33,38)(34,37)(35,36)(42,55)(43,67)(44,66)(45,65)(46,64)(47,63)(48,62)(49,61)(50,60)(51,59)(52,58)(53,57)(54,56)(69,80)(70,79)(71,78)(72,77)(73,76)(74,75);
s3 := Sym(82)!( 3,43)( 4,42)( 5,54)( 6,53)( 7,52)( 8,51)( 9,50)(10,49)(11,48)(12,47)(13,46)(14,45)(15,44)(16,56)(17,55)(18,67)(19,66)(20,65)(21,64)(22,63)(23,62)(24,61)(25,60)(26,59)(27,58)(28,57)(29,69)(30,68)(31,80)(32,79)(33,78)(34,77)(35,76)(36,75)(37,74)(38,73)(39,72)(40,71)(41,70);
s4 := Sym(82)!(81,82);
poly := sub<Sym(82)|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*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s1*s2*s3*s2*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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 >;