Part of the Atlas of Small Regular Polytopes

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

Atlas Canonical Name {2,2,4,4}*1568

Overview

Group
SmallGroup(1568,921)
Rank
5
Schläfli Type
{2,2,4,4}
Vertices, edges, …
2, 2, 49, 98, 49
Order of s0s1s2s3s4
14
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

No regular quotients.

Covers minimal covers in bold

None in this atlas.

Representations

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