Part of the Atlas of Small Regular Polytopes

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

Atlas Canonical Name {2,2,6,4}*576

Overview

Group
SmallGroup(576,8666)
Rank
5
Schläfli Type
{2,2,6,4}
Vertices, edges, …
2, 2, 18, 36, 12
Order of s0s1s2s3s4
4
Order of s0s1s2s3s4s3s2s1
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

2-fold

3-fold

Representations

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