Part of the Atlas of Small Regular Polytopes

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

Atlas Canonical Name {2,2,4,6,6}*1152e

Overview

Group
SmallGroup(1152,157863)
Rank
6
Schläfli Type
{2,2,4,6,6}
Vertices, edges, …
2, 2, 4, 12, 18, 6
Order of s0s1s2s3s4s5
6
Order of s0s1s2s3s4s5s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

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