Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,5,2,44}

Atlas Canonical Name {2,5,2,44}*1760

Overview

Group
SmallGroup(1760,1181)
Rank
5
Schläfli Type
{2,5,2,44}
Vertices, edges, …
2, 5, 5, 44, 44
Order of s0s1s2s3s4
220
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

11-fold

22-fold

Covers minimal covers in bold

None in this atlas.

Representations

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