Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1152,153175)
Rank
6
Schläfli Type
{2,4,6,6,2}
Vertices, edges, …
2, 4, 12, 18, 6, 2
Order of s0s1s2s3s4s5
12
Order of s0s1s2s3s4s5s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

3-fold

6-fold

9-fold

12-fold

18-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := (21,30)(22,31)(23,32)(24,33)(25,34)(26,35)(27,36)(28,37)(29,38);;
s2 := ( 3,21)( 4,22)( 5,23)( 6,27)( 7,28)( 8,29)( 9,24)(10,25)(11,26)(12,30)(13,31)(14,32)(15,36)(16,37)(17,38)(18,33)(19,34)(20,35);;
s3 := ( 3, 6)( 4, 8)( 5, 7)(10,11)(12,15)(13,17)(14,16)(19,20)(21,24)(22,26)(23,25)(28,29)(30,33)(31,35)(32,34)(37,38);;
s4 := ( 3, 4)( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)(30,31)(33,34)(36,37);;
s5 := (39,40);;
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, 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, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s4*s3*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(40)!(1,2);
s1 := Sym(40)!(21,30)(22,31)(23,32)(24,33)(25,34)(26,35)(27,36)(28,37)(29,38);
s2 := Sym(40)!( 3,21)( 4,22)( 5,23)( 6,27)( 7,28)( 8,29)( 9,24)(10,25)(11,26)(12,30)(13,31)(14,32)(15,36)(16,37)(17,38)(18,33)(19,34)(20,35);
s3 := Sym(40)!( 3, 6)( 4, 8)( 5, 7)(10,11)(12,15)(13,17)(14,16)(19,20)(21,24)(22,26)(23,25)(28,29)(30,33)(31,35)(32,34)(37,38);
s4 := Sym(40)!( 3, 4)( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)(30,31)(33,34)(36,37);
s5 := Sym(40)!(39,40);
poly := sub<Sym(40)|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, 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, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s4*s3*s2*s3*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;