Part of the Atlas of Small Regular Polytopes

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

Atlas Canonical Name {2,2,3,6,6}*1152

Overview

Group
SmallGroup(1152,157863)
Rank
6
Schläfli Type
{2,2,3,6,6}
Vertices, edges, …
2, 2, 4, 12, 24, 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

3-fold

6-fold

Covers minimal covers in bold

None in this atlas.

Representations

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