Part of the Atlas of Small Regular Polytopes

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

Atlas Canonical Name {2,2,4,4,6}*768

Overview

Group
SmallGroup(768,1076197)
Rank
6
Schläfli Type
{2,2,4,4,6}
Vertices, edges, …
2, 2, 4, 8, 12, 6
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

4-fold

6-fold

8-fold

12-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 5,17)( 6,18)( 7,19)( 8,20)( 9,21)(10,22)(11,23)(12,24)(13,25)(14,26)(15,27)(16,28)(29,41)(30,42)(31,43)(32,44)(33,45)(34,46)(35,47)(36,48)(37,49)(38,50)(39,51)(40,52);;
s3 := (17,23)(18,24)(19,25)(20,26)(21,27)(22,28)(29,32)(30,33)(31,34)(35,38)(36,39)(37,40)(41,50)(42,51)(43,52)(44,47)(45,48)(46,49);;
s4 := ( 5,29)( 6,31)( 7,30)( 8,32)( 9,34)(10,33)(11,35)(12,37)(13,36)(14,38)(15,40)(16,39)(17,41)(18,43)(19,42)(20,44)(21,46)(22,45)(23,47)(24,49)(25,48)(26,50)(27,52)(28,51);;
s5 := ( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)(32,33)(35,36)(38,39)(41,42)(44,45)(47,48)(50,51);;
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, s1*s2*s1*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, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, s3*s4*s5*s4*s3*s4*s5*s4, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(52)!(1,2);
s1 := Sym(52)!(3,4);
s2 := Sym(52)!( 5,17)( 6,18)( 7,19)( 8,20)( 9,21)(10,22)(11,23)(12,24)(13,25)(14,26)(15,27)(16,28)(29,41)(30,42)(31,43)(32,44)(33,45)(34,46)(35,47)(36,48)(37,49)(38,50)(39,51)(40,52);
s3 := Sym(52)!(17,23)(18,24)(19,25)(20,26)(21,27)(22,28)(29,32)(30,33)(31,34)(35,38)(36,39)(37,40)(41,50)(42,51)(43,52)(44,47)(45,48)(46,49);
s4 := Sym(52)!( 5,29)( 6,31)( 7,30)( 8,32)( 9,34)(10,33)(11,35)(12,37)(13,36)(14,38)(15,40)(16,39)(17,41)(18,43)(19,42)(20,44)(21,46)(22,45)(23,47)(24,49)(25,48)(26,50)(27,52)(28,51);
s5 := Sym(52)!( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)(32,33)(35,36)(38,39)(41,42)(44,45)(47,48)(50,51);
poly := sub<Sym(52)|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, 
s1*s2*s1*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, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s4*s5*s4*s3*s4*s5*s4, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;