Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,4,3,6,3,2}

Atlas Canonical Name {2,4,3,6,3,2}*1728

Overview

Group
SmallGroup(1728,46116)
Rank
7
Schläfli Type
{2,4,3,6,3,2}
Vertices, edges, …
2, 4, 6, 9, 9, 3, 2
Order of s0s1s2s3s4s5s6
6
Order of s0s1s2s3s4s5s6s5s4s3s2s1
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 := ( 3, 5)( 4, 6)( 7, 9)( 8,10)(11,13)(12,14)(15,17)(16,18)(19,21)(20,22)(23,25)(24,26)(27,29)(28,30)(31,33)(32,34)(35,37)(36,38);;
s2 := ( 4, 5)( 7,11)( 8,13)( 9,12)(10,14)(16,17)(19,23)(20,25)(21,24)(22,26)(28,29)(31,35)(32,37)(33,36)(34,38);;
s3 := ( 4, 6)( 7,11)( 8,14)( 9,13)(10,12)(15,23)(16,26)(17,25)(18,24)(20,22)(27,31)(28,34)(29,33)(30,32)(36,38);;
s4 := ( 3,15)( 4,16)( 5,17)( 6,18)( 7,23)( 8,24)( 9,25)(10,26)(11,19)(12,20)(13,21)(14,22)(31,35)(32,36)(33,37)(34,38);;
s5 := ( 7,11)( 8,12)( 9,13)(10,14)(15,27)(16,28)(17,29)(18,30)(19,35)(20,36)(21,37)(22,38)(23,31)(24,32)(25,33)(26,34);;
s6 := (39,40);;
poly := Group([s0,s1,s2,s3,s4,s5,s6]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4","s5","s6");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  s6 := F.7;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s6*s6, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*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, s0*s6*s0*s6, 
s1*s6*s1*s6, s2*s6*s2*s6, s3*s6*s3*s6, 
s4*s6*s4*s6, s5*s6*s5*s6, s2*s3*s2*s3*s2*s3, 
s4*s5*s4*s5*s4*s5, s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s1*s2*s3*s1*s2, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, 
s3*s4*s5*s3*s4*s3*s4*s5*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(40)!(1,2);
s1 := Sym(40)!( 3, 5)( 4, 6)( 7, 9)( 8,10)(11,13)(12,14)(15,17)(16,18)(19,21)(20,22)(23,25)(24,26)(27,29)(28,30)(31,33)(32,34)(35,37)(36,38);
s2 := Sym(40)!( 4, 5)( 7,11)( 8,13)( 9,12)(10,14)(16,17)(19,23)(20,25)(21,24)(22,26)(28,29)(31,35)(32,37)(33,36)(34,38);
s3 := Sym(40)!( 4, 6)( 7,11)( 8,14)( 9,13)(10,12)(15,23)(16,26)(17,25)(18,24)(20,22)(27,31)(28,34)(29,33)(30,32)(36,38);
s4 := Sym(40)!( 3,15)( 4,16)( 5,17)( 6,18)( 7,23)( 8,24)( 9,25)(10,26)(11,19)(12,20)(13,21)(14,22)(31,35)(32,36)(33,37)(34,38);
s5 := Sym(40)!( 7,11)( 8,12)( 9,13)(10,14)(15,27)(16,28)(17,29)(18,30)(19,35)(20,36)(21,37)(22,38)(23,31)(24,32)(25,33)(26,34);
s6 := Sym(40)!(39,40);
poly := sub<Sym(40)|s0,s1,s2,s3,s4,s5,s6>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4,s5,s6> := Group< s0,s1,s2,s3,s4,s5,s6 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s6*s6, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*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, s0*s6*s0*s6, s1*s6*s1*s6, 
s2*s6*s2*s6, s3*s6*s3*s6, s4*s6*s4*s6, 
s5*s6*s5*s6, s2*s3*s2*s3*s2*s3, s4*s5*s4*s5*s4*s5, 
s1*s2*s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s3*s4*s5*s3*s4*s3*s4*s5*s3*s4 >;