Part of the Atlas of Small Regular Polytopes

Polytope of Type {13,2,9,4}

Atlas Canonical Name {13,2,9,4}*1872

Overview

Group
SmallGroup(1872,539)
Rank
5
Schläfli Type
{13,2,9,4}
Vertices, edges, …
13, 13, 9, 18, 4
Order of s0s1s2s3s4
117
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

3-fold

Covers minimal covers in bold

None in this atlas.

Representations

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