Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1728,46139)
Rank
5
Schläfli Type
{2,2,12,4}
Vertices, edges, …
2, 2, 54, 108, 18
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 := (3,4);;
s2 := ( 6, 7)( 9,10)(12,13)(14,23)(15,25)(16,24)(17,26)(18,28)(19,27)(20,29)(21,31)(22,30)(33,34)(36,37)(39,40)(41,50)(42,52)(43,51)(44,53)(45,55)(46,54)(47,56)(48,58)(49,57);;
s3 := ( 5, 6)( 8,24)( 9,23)(10,25)(11,15)(12,14)(13,16)(17,31)(18,30)(19,29)(21,22)(27,28)(32,33)(35,51)(36,50)(37,52)(38,42)(39,41)(40,43)(44,58)(45,57)(46,56)(48,49)(54,55);;
s4 := ( 5,35)( 6,37)( 7,36)( 8,32)( 9,34)(10,33)(11,38)(12,40)(13,39)(14,44)(15,46)(16,45)(17,41)(18,43)(19,42)(20,47)(21,49)(22,48)(23,53)(24,55)(25,54)(26,50)(27,52)(28,51)(29,56)(30,58)(31,57);;
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, s1*s2*s1*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*s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3*s4*s2*s3*s2*s3*s2*s3*s2*s3*s4*s2*s3, 
s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(58)!(1,2);
s1 := Sym(58)!(3,4);
s2 := Sym(58)!( 6, 7)( 9,10)(12,13)(14,23)(15,25)(16,24)(17,26)(18,28)(19,27)(20,29)(21,31)(22,30)(33,34)(36,37)(39,40)(41,50)(42,52)(43,51)(44,53)(45,55)(46,54)(47,56)(48,58)(49,57);
s3 := Sym(58)!( 5, 6)( 8,24)( 9,23)(10,25)(11,15)(12,14)(13,16)(17,31)(18,30)(19,29)(21,22)(27,28)(32,33)(35,51)(36,50)(37,52)(38,42)(39,41)(40,43)(44,58)(45,57)(46,56)(48,49)(54,55);
s4 := Sym(58)!( 5,35)( 6,37)( 7,36)( 8,32)( 9,34)(10,33)(11,38)(12,40)(13,39)(14,44)(15,46)(16,45)(17,41)(18,43)(19,42)(20,47)(21,49)(22,48)(23,53)(24,55)(25,54)(26,50)(27,52)(28,51)(29,56)(30,58)(31,57);
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, 
s1*s2*s1*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*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s4*s2*s3*s2*s3*s2*s3*s2*s3*s4*s2*s3, 
s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3 >;