Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1728,47887)
Rank
6
Schläfli Type
{3,2,4,6,2}
Vertices, edges, …
3, 3, 12, 36, 18, 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

9-fold

18-fold

Covers minimal covers in bold

None in this atlas.

Representations

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