Part of the Atlas of Small Regular Polytopes

Polytope of Type {11,2,4,9}

Atlas Canonical Name {11,2,4,9}*1584

Overview

Group
SmallGroup(1584,364)
Rank
5
Schläfli Type
{11,2,4,9}
Vertices, edges, …
11, 11, 4, 18, 9
Order of s0s1s2s3s4
99
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);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10);;
s2 := (13,18)(14,20)(15,22)(16,24)(19,29)(21,31)(25,35)(32,41)(34,43)(36,44)(38,45)(40,46);;
s3 := (12,13)(14,17)(15,16)(18,26)(19,25)(20,27)(21,23)(22,24)(28,34)(29,35)(30,32)(31,33)(36,42)(37,43)(38,40)(39,41)(44,47)(45,46);;
s4 := (12,17)(13,15)(14,25)(16,21)(18,22)(19,34)(20,35)(23,30)(24,31)(26,27)(28,42)(29,43)(32,38)(33,39)(36,40)(37,47)(41,45)(44,46);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
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(47)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11);
s1 := Sym(47)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10);
s2 := Sym(47)!(13,18)(14,20)(15,22)(16,24)(19,29)(21,31)(25,35)(32,41)(34,43)(36,44)(38,45)(40,46);
s3 := Sym(47)!(12,13)(14,17)(15,16)(18,26)(19,25)(20,27)(21,23)(22,24)(28,34)(29,35)(30,32)(31,33)(36,42)(37,43)(38,40)(39,41)(44,47)(45,46);
s4 := Sym(47)!(12,17)(13,15)(14,25)(16,21)(18,22)(19,34)(20,35)(23,30)(24,31)(26,27)(28,42)(29,43)(32,38)(33,39)(36,40)(37,47)(41,45)(44,46);
poly := sub<Sym(47)|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, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;