Part of the Atlas of Small Regular Polytopes

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

Atlas Canonical Name {2,12,4,2}*1728a

Overview

Group
SmallGroup(1728,46139)
Rank
5
Schläfli Type
{2,12,4,2}
Vertices, edges, …
2, 54, 108, 18, 2
Order of s0s1s2s3s4
6
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

3-fold

6-fold

54-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := ( 4, 5)( 7, 8)(10,11)(12,21)(13,23)(14,22)(15,24)(16,26)(17,25)(18,27)(19,29)(20,28)(31,32)(34,35)(37,38)(39,48)(40,50)(41,49)(42,51)(43,53)(44,52)(45,54)(46,56)(47,55);;
s2 := ( 3, 4)( 6,22)( 7,21)( 8,23)( 9,13)(10,12)(11,14)(15,29)(16,28)(17,27)(19,20)(25,26)(30,31)(33,49)(34,48)(35,50)(36,40)(37,39)(38,41)(42,56)(43,55)(44,54)(46,47)(52,53);;
s3 := ( 3,33)( 4,35)( 5,34)( 6,30)( 7,32)( 8,31)( 9,36)(10,38)(11,37)(12,42)(13,44)(14,43)(15,39)(16,41)(17,40)(18,45)(19,47)(20,46)(21,51)(22,53)(23,52)(24,48)(25,50)(26,49)(27,54)(28,56)(29,55);;
s4 := (57,58);;
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, 
s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(58)!(1,2);
s1 := Sym(58)!( 4, 5)( 7, 8)(10,11)(12,21)(13,23)(14,22)(15,24)(16,26)(17,25)(18,27)(19,29)(20,28)(31,32)(34,35)(37,38)(39,48)(40,50)(41,49)(42,51)(43,53)(44,52)(45,54)(46,56)(47,55);
s2 := Sym(58)!( 3, 4)( 6,22)( 7,21)( 8,23)( 9,13)(10,12)(11,14)(15,29)(16,28)(17,27)(19,20)(25,26)(30,31)(33,49)(34,48)(35,50)(36,40)(37,39)(38,41)(42,56)(43,55)(44,54)(46,47)(52,53);
s3 := Sym(58)!( 3,33)( 4,35)( 5,34)( 6,30)( 7,32)( 8,31)( 9,36)(10,38)(11,37)(12,42)(13,44)(14,43)(15,39)(16,41)(17,40)(18,45)(19,47)(20,46)(21,51)(22,53)(23,52)(24,48)(25,50)(26,49)(27,54)(28,56)(29,55);
s4 := Sym(58)!(57,58);
poly := sub<Sym(58)|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, s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 >;