Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,52,6}

Atlas Canonical Name {2,52,6}*1248b

Overview

Group
SmallGroup(1248,1438)
Rank
4
Schläfli Type
{2,52,6}
Vertices, edges, …
2, 52, 156, 6
Order of s0s1s2s3
78
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

13-fold

26-fold

Covers minimal covers in bold

None in this atlas.

Representations

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