Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,5,2,9,4}

Atlas Canonical Name {2,5,2,9,4}*1440

Overview

Group
SmallGroup(1440,4569)
Rank
6
Schläfli Type
{2,5,2,9,4}
Vertices, edges, …
2, 5, 5, 9, 18, 4
Order of s0s1s2s3s4s5
90
Order of s0s1s2s3s4s5s4s3s2s1
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 := (1,2);;
s1 := (4,5)(6,7);;
s2 := (3,4)(5,6);;
s3 := ( 8, 9)(10,13)(11,12)(14,22)(15,21)(16,23)(17,19)(18,20)(24,30)(25,31)(26,28)(27,29)(32,38)(33,39)(34,36)(35,37)(40,43)(41,42);;
s4 := ( 8,12)( 9,10)(11,19)(13,15)(14,16)(17,28)(18,29)(20,22)(21,24)(23,25)(26,36)(27,37)(30,32)(31,33)(34,38)(35,42)(39,40)(41,43);;
s5 := ( 8,22)( 9,14)(10,16)(13,23)(17,27)(19,29)(24,33)(26,35)(28,37)(30,39)(32,40)(38,43);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
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, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5*s4*s5*s4*s5, s5*s4*s3*s5*s4*s5*s4*s3*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 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(43)!(1,2);
s1 := Sym(43)!(4,5)(6,7);
s2 := Sym(43)!(3,4)(5,6);
s3 := Sym(43)!( 8, 9)(10,13)(11,12)(14,22)(15,21)(16,23)(17,19)(18,20)(24,30)(25,31)(26,28)(27,29)(32,38)(33,39)(34,36)(35,37)(40,43)(41,42);
s4 := Sym(43)!( 8,12)( 9,10)(11,19)(13,15)(14,16)(17,28)(18,29)(20,22)(21,24)(23,25)(26,36)(27,37)(30,32)(31,33)(34,38)(35,42)(39,40)(41,43);
s5 := Sym(43)!( 8,22)( 9,14)(10,16)(13,23)(17,27)(19,29)(24,33)(26,35)(28,37)(30,39)(32,40)(38,43);
poly := sub<Sym(43)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, 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, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5*s4*s5*s4*s5, 
s5*s4*s3*s5*s4*s5*s4*s3*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 >;