Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1728,47887)
Rank
6
Schläfli Type
{3,2,2,6,4}
Vertices, edges, …
3, 3, 2, 18, 36, 12
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 := (4,5);;
s3 := ( 6,33)( 7,35)( 8,34)( 9,39)(10,41)(11,40)(12,36)(13,38)(14,37)(15,24)(16,26)(17,25)(18,30)(19,32)(20,31)(21,27)(22,29)(23,28)(42,69)(43,71)(44,70)(45,75)(46,77)(47,76)(48,72)(49,74)(50,73)(51,60)(52,62)(53,61)(54,66)(55,68)(56,67)(57,63)(58,65)(59,64);;
s4 := ( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(24,27)(25,28)(26,29)(33,36)(34,37)(35,38)(42,54)(43,55)(44,56)(45,51)(46,52)(47,53)(48,57)(49,58)(50,59)(60,72)(61,73)(62,74)(63,69)(64,70)(65,71)(66,75)(67,76)(68,77);;
s5 := ( 6,42)( 7,45)( 8,48)( 9,43)(10,46)(11,49)(12,44)(13,47)(14,50)(15,51)(16,54)(17,57)(18,52)(19,55)(20,58)(21,53)(22,56)(23,59)(24,60)(25,63)(26,66)(27,61)(28,64)(29,67)(30,62)(31,65)(32,68)(33,69)(34,72)(35,75)(36,70)(37,73)(38,76)(39,71)(40,74)(41,77);;
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, 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, 
s0*s1*s0*s1*s0*s1, s4*s5*s4*s5*s4*s5*s4*s5, 
s5*s3*s4*s5*s3*s4*s5*s3*s4*s5*s3*s4, 
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)!(4,5);
s3 := Sym(77)!( 6,33)( 7,35)( 8,34)( 9,39)(10,41)(11,40)(12,36)(13,38)(14,37)(15,24)(16,26)(17,25)(18,30)(19,32)(20,31)(21,27)(22,29)(23,28)(42,69)(43,71)(44,70)(45,75)(46,77)(47,76)(48,72)(49,74)(50,73)(51,60)(52,62)(53,61)(54,66)(55,68)(56,67)(57,63)(58,65)(59,64);
s4 := Sym(77)!( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(24,27)(25,28)(26,29)(33,36)(34,37)(35,38)(42,54)(43,55)(44,56)(45,51)(46,52)(47,53)(48,57)(49,58)(50,59)(60,72)(61,73)(62,74)(63,69)(64,70)(65,71)(66,75)(67,76)(68,77);
s5 := Sym(77)!( 6,42)( 7,45)( 8,48)( 9,43)(10,46)(11,49)(12,44)(13,47)(14,50)(15,51)(16,54)(17,57)(18,52)(19,55)(20,58)(21,53)(22,56)(23,59)(24,60)(25,63)(26,66)(27,61)(28,64)(29,67)(30,62)(31,65)(32,68)(33,69)(34,72)(35,75)(36,70)(37,73)(38,76)(39,71)(40,74)(41,77);
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, 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, s0*s1*s0*s1*s0*s1, s4*s5*s4*s5*s4*s5*s4*s5, 
s5*s3*s4*s5*s3*s4*s5*s3*s4*s5*s3*s4, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;