Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,3,2,12,6}

Atlas Canonical Name {2,3,2,12,6}*1728a

Overview

Group
SmallGroup(1728,47319)
Rank
6
Schläfli Type
{2,3,2,12,6}
Vertices, edges, …
2, 3, 3, 12, 36, 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

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 := (4,5);;
s2 := (3,4);;
s3 := ( 6,42)( 7,43)( 8,44)( 9,48)(10,49)(11,50)(12,45)(13,46)(14,47)(15,51)(16,52)(17,53)(18,57)(19,58)(20,59)(21,54)(22,55)(23,56)(24,69)(25,70)(26,71)(27,75)(28,76)(29,77)(30,72)(31,73)(32,74)(33,60)(34,61)(35,62)(36,66)(37,67)(38,68)(39,63)(40,64)(41,65);;
s4 := ( 6,63)( 7,65)( 8,64)( 9,60)(10,62)(11,61)(12,66)(13,68)(14,67)(15,72)(16,74)(17,73)(18,69)(19,71)(20,70)(21,75)(22,77)(23,76)(24,45)(25,47)(26,46)(27,42)(28,44)(29,43)(30,48)(31,50)(32,49)(33,54)(34,56)(35,55)(36,51)(37,53)(38,52)(39,57)(40,59)(41,58);;
s5 := ( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)(30,31)(33,34)(36,37)(39,40)(42,43)(45,46)(48,49)(51,52)(54,55)(57,58)(60,61)(63,64)(66,67)(69,70)(72,73)(75,76);;
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, s2*s3*s2*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, 
s1*s2*s1*s2*s1*s2, s3*s4*s5*s4*s3*s4*s5*s4, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(77)!(1,2);
s1 := Sym(77)!(4,5);
s2 := Sym(77)!(3,4);
s3 := Sym(77)!( 6,42)( 7,43)( 8,44)( 9,48)(10,49)(11,50)(12,45)(13,46)(14,47)(15,51)(16,52)(17,53)(18,57)(19,58)(20,59)(21,54)(22,55)(23,56)(24,69)(25,70)(26,71)(27,75)(28,76)(29,77)(30,72)(31,73)(32,74)(33,60)(34,61)(35,62)(36,66)(37,67)(38,68)(39,63)(40,64)(41,65);
s4 := Sym(77)!( 6,63)( 7,65)( 8,64)( 9,60)(10,62)(11,61)(12,66)(13,68)(14,67)(15,72)(16,74)(17,73)(18,69)(19,71)(20,70)(21,75)(22,77)(23,76)(24,45)(25,47)(26,46)(27,42)(28,44)(29,43)(30,48)(31,50)(32,49)(33,54)(34,56)(35,55)(36,51)(37,53)(38,52)(39,57)(40,59)(41,58);
s5 := Sym(77)!( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)(30,31)(33,34)(36,37)(39,40)(42,43)(45,46)(48,49)(51,52)(54,55)(57,58)(60,61)(63,64)(66,67)(69,70)(72,73)(75,76);
poly := sub<Sym(77)|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, s2*s3*s2*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, s1*s2*s1*s2*s1*s2, s3*s4*s5*s4*s3*s4*s5*s4, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;