Part of the Atlas of Small Regular Polytopes

Polytope of Type {18,9,2,3}

Atlas Canonical Name {18,9,2,3}*1944

Overview

Group
SmallGroup(1944,2339)
Rank
5
Schläfli Type
{18,9,2,3}
Vertices, edges, …
18, 81, 9, 3, 3
Order of s0s1s2s3s4
18
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

3-fold

9-fold

27-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := ( 4, 7)( 5, 8)( 6, 9)(13,16)(14,17)(15,18)(22,25)(23,26)(24,27)(28,58)(29,59)(30,60)(31,55)(32,56)(33,57)(34,61)(35,62)(36,63)(37,67)(38,68)(39,69)(40,64)(41,65)(42,66)(43,70)(44,71)(45,72)(46,76)(47,77)(48,78)(49,73)(50,74)(51,75)(52,79)(53,80)(54,81);;
s1 := ( 1,28)( 2,30)( 3,29)( 4,34)( 5,36)( 6,35)( 7,31)( 8,33)( 9,32)(10,47)(11,46)(12,48)(13,53)(14,52)(15,54)(16,50)(17,49)(18,51)(19,38)(20,37)(21,39)(22,44)(23,43)(24,45)(25,41)(26,40)(27,42)(55,58)(56,60)(57,59)(62,63)(64,77)(65,76)(66,78)(67,74)(68,73)(69,75)(70,80)(71,79)(72,81);;
s2 := ( 1,10)( 2,12)( 3,11)( 4,16)( 5,18)( 6,17)( 7,13)( 8,15)( 9,14)(19,20)(22,26)(23,25)(24,27)(28,67)(29,69)(30,68)(31,64)(32,66)(33,65)(34,70)(35,72)(36,71)(37,58)(38,60)(39,59)(40,55)(41,57)(42,56)(43,61)(44,63)(45,62)(46,77)(47,76)(48,78)(49,74)(50,73)(51,75)(52,80)(53,79)(54,81);;
s3 := (83,84);;
s4 := (82,83);;
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*s2*s0*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, 
s3*s4*s3*s4*s3*s4, s0*s1*s2*s0*s1*s0*s1*s2*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(84)!( 4, 7)( 5, 8)( 6, 9)(13,16)(14,17)(15,18)(22,25)(23,26)(24,27)(28,58)(29,59)(30,60)(31,55)(32,56)(33,57)(34,61)(35,62)(36,63)(37,67)(38,68)(39,69)(40,64)(41,65)(42,66)(43,70)(44,71)(45,72)(46,76)(47,77)(48,78)(49,73)(50,74)(51,75)(52,79)(53,80)(54,81);
s1 := Sym(84)!( 1,28)( 2,30)( 3,29)( 4,34)( 5,36)( 6,35)( 7,31)( 8,33)( 9,32)(10,47)(11,46)(12,48)(13,53)(14,52)(15,54)(16,50)(17,49)(18,51)(19,38)(20,37)(21,39)(22,44)(23,43)(24,45)(25,41)(26,40)(27,42)(55,58)(56,60)(57,59)(62,63)(64,77)(65,76)(66,78)(67,74)(68,73)(69,75)(70,80)(71,79)(72,81);
s2 := Sym(84)!( 1,10)( 2,12)( 3,11)( 4,16)( 5,18)( 6,17)( 7,13)( 8,15)( 9,14)(19,20)(22,26)(23,25)(24,27)(28,67)(29,69)(30,68)(31,64)(32,66)(33,65)(34,70)(35,72)(36,71)(37,58)(38,60)(39,59)(40,55)(41,57)(42,56)(43,61)(44,63)(45,62)(46,77)(47,76)(48,78)(49,74)(50,73)(51,75)(52,80)(53,79)(54,81);
s3 := Sym(84)!(83,84);
s4 := Sym(84)!(82,83);
poly := sub<Sym(84)|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*s2*s0*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, s3*s4*s3*s4*s3*s4, 
s0*s1*s2*s0*s1*s0*s1*s2*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;