Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,4,6,12}

Atlas Canonical Name {2,4,6,12}*1152f

Overview

Group
SmallGroup(1152,157864)
Rank
5
Schläfli Type
{2,4,6,12}
Vertices, edges, …
2, 4, 12, 36, 12
Order of s0s1s2s3s4
6
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

6-fold

Covers minimal covers in bold

None in this atlas.

Representations

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