Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1152,153182)
Rank
6
Schläfli Type
{2,2,2,6,4}
Vertices, edges, …
2, 2, 2, 18, 36, 12
Order of s0s1s2s3s4s5
4
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 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := ( 7,34)( 8,36)( 9,35)(10,40)(11,42)(12,41)(13,37)(14,39)(15,38)(16,25)(17,27)(18,26)(19,31)(20,33)(21,32)(22,28)(23,30)(24,29)(43,70)(44,72)(45,71)(46,76)(47,78)(48,77)(49,73)(50,75)(51,74)(52,61)(53,63)(54,62)(55,67)(56,69)(57,68)(58,64)(59,66)(60,65);;
s4 := ( 7,10)( 8,11)( 9,12)(16,19)(17,20)(18,21)(25,28)(26,29)(27,30)(34,37)(35,38)(36,39)(43,55)(44,56)(45,57)(46,52)(47,53)(48,54)(49,58)(50,59)(51,60)(61,73)(62,74)(63,75)(64,70)(65,71)(66,72)(67,76)(68,77)(69,78);;
s5 := ( 7,43)( 8,46)( 9,49)(10,44)(11,47)(12,50)(13,45)(14,48)(15,51)(16,52)(17,55)(18,58)(19,53)(20,56)(21,59)(22,54)(23,57)(24,60)(25,61)(26,64)(27,67)(28,62)(29,65)(30,68)(31,63)(32,66)(33,69)(34,70)(35,73)(36,76)(37,71)(38,74)(39,77)(40,72)(41,75)(42,78);;
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, 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, 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(78)!(1,2);
s1 := Sym(78)!(3,4);
s2 := Sym(78)!(5,6);
s3 := Sym(78)!( 7,34)( 8,36)( 9,35)(10,40)(11,42)(12,41)(13,37)(14,39)(15,38)(16,25)(17,27)(18,26)(19,31)(20,33)(21,32)(22,28)(23,30)(24,29)(43,70)(44,72)(45,71)(46,76)(47,78)(48,77)(49,73)(50,75)(51,74)(52,61)(53,63)(54,62)(55,67)(56,69)(57,68)(58,64)(59,66)(60,65);
s4 := Sym(78)!( 7,10)( 8,11)( 9,12)(16,19)(17,20)(18,21)(25,28)(26,29)(27,30)(34,37)(35,38)(36,39)(43,55)(44,56)(45,57)(46,52)(47,53)(48,54)(49,58)(50,59)(51,60)(61,73)(62,74)(63,75)(64,70)(65,71)(66,72)(67,76)(68,77)(69,78);
s5 := Sym(78)!( 7,43)( 8,46)( 9,49)(10,44)(11,47)(12,50)(13,45)(14,48)(15,51)(16,52)(17,55)(18,58)(19,53)(20,56)(21,59)(22,54)(23,57)(24,60)(25,61)(26,64)(27,67)(28,62)(29,65)(30,68)(31,63)(32,66)(33,69)(34,70)(35,73)(36,76)(37,71)(38,74)(39,77)(40,72)(41,75)(42,78);
poly := sub<Sym(78)|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, 
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, 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 >;