Part of the Atlas of Small Regular Polytopes

Polytope of Type {7,2,4,9}

Atlas Canonical Name {7,2,4,9}*1008

Overview

Group
SmallGroup(1008,500)
Rank
5
Schläfli Type
{7,2,4,9}
Vertices, edges, …
7, 7, 4, 18, 9
Order of s0s1s2s3s4
63
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);;
s1 := (1,2)(3,4)(5,6);;
s2 := ( 9,14)(10,16)(11,18)(12,20)(15,25)(17,27)(21,31)(28,37)(30,39)(32,40)(34,41)(36,42);;
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 := ( 8,13)( 9,11)(10,21)(12,17)(14,18)(15,30)(16,31)(19,26)(20,27)(22,23)(24,38)(25,39)(28,34)(29,35)(32,36)(33,43)(37,41)(40,42);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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)!(2,3)(4,5)(6,7);
s1 := Sym(43)!(1,2)(3,4)(5,6);
s2 := Sym(43)!( 9,14)(10,16)(11,18)(12,20)(15,25)(17,27)(21,31)(28,37)(30,39)(32,40)(34,41)(36,42);
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)!( 8,13)( 9,11)(10,21)(12,17)(14,18)(15,30)(16,31)(19,26)(20,27)(22,23)(24,38)(25,39)(28,34)(29,35)(32,36)(33,43)(37,41)(40,42);
poly := sub<Sym(43)|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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;