Part of the Atlas of Small Regular Polytopes

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

Atlas Canonical Name {2,4,6,4}*1152a

Overview

Group
SmallGroup(1152,136369)
Rank
5
Schläfli Type
{2,4,6,4}
Vertices, edges, …
2, 12, 36, 36, 4
Order of s0s1s2s3s4
4
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

4-fold

9-fold

18-fold

36-fold

Covers minimal covers in bold

None in this atlas.

Representations

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