Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,4,6,3,2,3}

Atlas Canonical Name {2,4,6,3,2,3}*1728

Overview

Group
SmallGroup(1728,47409)
Rank
7
Schläfli Type
{2,4,6,3,2,3}
Vertices, edges, …
2, 4, 12, 9, 3, 3, 3
Order of s0s1s2s3s4s5s6
12
Order of s0s1s2s3s4s5s6s5s4s3s2s1
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

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := ( 3,21)( 4,22)( 5,23)( 6,24)( 7,25)( 8,26)( 9,27)(10,28)(11,29)(12,30)(13,31)(14,32)(15,33)(16,34)(17,35)(18,36)(19,37)(20,38)(39,57)(40,58)(41,59)(42,60)(43,61)(44,62)(45,63)(46,64)(47,65)(48,66)(49,67)(50,68)(51,69)(52,70)(53,71)(54,72)(55,73)(56,74);;
s2 := ( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(21,30)(22,32)(23,31)(24,33)(25,35)(26,34)(27,36)(28,38)(29,37)(40,41)(43,44)(46,47)(49,50)(52,53)(55,56)(57,66)(58,68)(59,67)(60,69)(61,71)(62,70)(63,72)(64,74)(65,73);;
s3 := ( 3,40)( 4,39)( 5,41)( 6,46)( 7,45)( 8,47)( 9,43)(10,42)(11,44)(12,49)(13,48)(14,50)(15,55)(16,54)(17,56)(18,52)(19,51)(20,53)(21,58)(22,57)(23,59)(24,64)(25,63)(26,65)(27,61)(28,60)(29,62)(30,67)(31,66)(32,68)(33,73)(34,72)(35,74)(36,70)(37,69)(38,71);;
s4 := ( 3,42)( 4,44)( 5,43)( 6,39)( 7,41)( 8,40)( 9,45)(10,47)(11,46)(12,51)(13,53)(14,52)(15,48)(16,50)(17,49)(18,54)(19,56)(20,55)(21,60)(22,62)(23,61)(24,57)(25,59)(26,58)(27,63)(28,65)(29,64)(30,69)(31,71)(32,70)(33,66)(34,68)(35,67)(36,72)(37,74)(38,73);;
s5 := (76,77);;
s6 := (75,76);;
poly := Group([s0,s1,s2,s3,s4,s5,s6]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4","s5","s6");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  s6 := F.7;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s6*s6, 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, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5, 
s0*s6*s0*s6, s1*s6*s1*s6, s2*s6*s2*s6, 
s3*s6*s3*s6, s4*s6*s4*s6, s3*s4*s3*s4*s3*s4, 
s5*s6*s5*s6*s5*s6, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s4*s2*s3*s2*s3*s4*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(77)!(1,2);
s1 := Sym(77)!( 3,21)( 4,22)( 5,23)( 6,24)( 7,25)( 8,26)( 9,27)(10,28)(11,29)(12,30)(13,31)(14,32)(15,33)(16,34)(17,35)(18,36)(19,37)(20,38)(39,57)(40,58)(41,59)(42,60)(43,61)(44,62)(45,63)(46,64)(47,65)(48,66)(49,67)(50,68)(51,69)(52,70)(53,71)(54,72)(55,73)(56,74);
s2 := Sym(77)!( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(21,30)(22,32)(23,31)(24,33)(25,35)(26,34)(27,36)(28,38)(29,37)(40,41)(43,44)(46,47)(49,50)(52,53)(55,56)(57,66)(58,68)(59,67)(60,69)(61,71)(62,70)(63,72)(64,74)(65,73);
s3 := Sym(77)!( 3,40)( 4,39)( 5,41)( 6,46)( 7,45)( 8,47)( 9,43)(10,42)(11,44)(12,49)(13,48)(14,50)(15,55)(16,54)(17,56)(18,52)(19,51)(20,53)(21,58)(22,57)(23,59)(24,64)(25,63)(26,65)(27,61)(28,60)(29,62)(30,67)(31,66)(32,68)(33,73)(34,72)(35,74)(36,70)(37,69)(38,71);
s4 := Sym(77)!( 3,42)( 4,44)( 5,43)( 6,39)( 7,41)( 8,40)( 9,45)(10,47)(11,46)(12,51)(13,53)(14,52)(15,48)(16,50)(17,49)(18,54)(19,56)(20,55)(21,60)(22,62)(23,61)(24,57)(25,59)(26,58)(27,63)(28,65)(29,64)(30,69)(31,71)(32,70)(33,66)(34,68)(35,67)(36,72)(37,74)(38,73);
s5 := Sym(77)!(76,77);
s6 := Sym(77)!(75,76);
poly := sub<Sym(77)|s0,s1,s2,s3,s4,s5,s6>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4,s5,s6> := Group< s0,s1,s2,s3,s4,s5,s6 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s6*s6, 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, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5, s0*s6*s0*s6, 
s1*s6*s1*s6, s2*s6*s2*s6, s3*s6*s3*s6, 
s4*s6*s4*s6, s3*s4*s3*s4*s3*s4, s5*s6*s5*s6*s5*s6, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s4*s2*s3*s2*s3*s4*s2*s3 >;