Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1728,47319)
Rank
6
Schläfli Type
{3,2,12,6,2}
Vertices, edges, …
3, 3, 12, 36, 6, 2
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 := (2,3);;
s1 := (1,2);;
s2 := ( 4,40)( 5,41)( 6,42)( 7,46)( 8,47)( 9,48)(10,43)(11,44)(12,45)(13,49)(14,50)(15,51)(16,55)(17,56)(18,57)(19,52)(20,53)(21,54)(22,67)(23,68)(24,69)(25,73)(26,74)(27,75)(28,70)(29,71)(30,72)(31,58)(32,59)(33,60)(34,64)(35,65)(36,66)(37,61)(38,62)(39,63);;
s3 := ( 4,61)( 5,63)( 6,62)( 7,58)( 8,60)( 9,59)(10,64)(11,66)(12,65)(13,70)(14,72)(15,71)(16,67)(17,69)(18,68)(19,73)(20,75)(21,74)(22,43)(23,45)(24,44)(25,40)(26,42)(27,41)(28,46)(29,48)(30,47)(31,52)(32,54)(33,53)(34,49)(35,51)(36,50)(37,55)(38,57)(39,56);;
s4 := ( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)(34,35)(37,38)(40,41)(43,44)(46,47)(49,50)(52,53)(55,56)(58,59)(61,62)(64,65)(67,68)(70,71)(73,74);;
s5 := (76,77);;
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*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, s4*s5*s4*s5, 
s0*s1*s0*s1*s0*s1, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(77)!(2,3);
s1 := Sym(77)!(1,2);
s2 := Sym(77)!( 4,40)( 5,41)( 6,42)( 7,46)( 8,47)( 9,48)(10,43)(11,44)(12,45)(13,49)(14,50)(15,51)(16,55)(17,56)(18,57)(19,52)(20,53)(21,54)(22,67)(23,68)(24,69)(25,73)(26,74)(27,75)(28,70)(29,71)(30,72)(31,58)(32,59)(33,60)(34,64)(35,65)(36,66)(37,61)(38,62)(39,63);
s3 := Sym(77)!( 4,61)( 5,63)( 6,62)( 7,58)( 8,60)( 9,59)(10,64)(11,66)(12,65)(13,70)(14,72)(15,71)(16,67)(17,69)(18,68)(19,73)(20,75)(21,74)(22,43)(23,45)(24,44)(25,40)(26,42)(27,41)(28,46)(29,48)(30,47)(31,52)(32,54)(33,53)(34,49)(35,51)(36,50)(37,55)(38,57)(39,56);
s4 := Sym(77)!( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)(34,35)(37,38)(40,41)(43,44)(46,47)(49,50)(52,53)(55,56)(58,59)(61,62)(64,65)(67,68)(70,71)(73,74);
s5 := Sym(77)!(76,77);
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*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, 
s4*s5*s4*s5, s0*s1*s0*s1*s0*s1, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;