Part of the Atlas of Small Regular Polytopes

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

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

Overview

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

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat
  • Self-Dual

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