Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1944,2339)
Rank
5
Schläfli Type
{9,18,2,3}
Vertices, edges, …
9, 81, 18, 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 := ( 2, 3)( 4, 7)( 5, 9)( 6, 8)(10,20)(11,19)(12,21)(13,26)(14,25)(15,27)(16,23)(17,22)(18,24)(28,58)(29,60)(30,59)(31,55)(32,57)(33,56)(34,61)(35,63)(36,62)(37,77)(38,76)(39,78)(40,74)(41,73)(42,75)(43,80)(44,79)(45,81)(46,68)(47,67)(48,69)(49,65)(50,64)(51,66)(52,71)(53,70)(54,72);;
s1 := ( 1,37)( 2,39)( 3,38)( 4,43)( 5,45)( 6,44)( 7,40)( 8,42)( 9,41)(10,28)(11,30)(12,29)(13,34)(14,36)(15,35)(16,31)(17,33)(18,32)(19,47)(20,46)(21,48)(22,53)(23,52)(24,54)(25,50)(26,49)(27,51)(55,67)(56,69)(57,68)(58,64)(59,66)(60,65)(61,70)(62,72)(63,71)(73,77)(74,76)(75,78)(79,80);;
s2 := ( 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);;
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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(84)!( 2, 3)( 4, 7)( 5, 9)( 6, 8)(10,20)(11,19)(12,21)(13,26)(14,25)(15,27)(16,23)(17,22)(18,24)(28,58)(29,60)(30,59)(31,55)(32,57)(33,56)(34,61)(35,63)(36,62)(37,77)(38,76)(39,78)(40,74)(41,73)(42,75)(43,80)(44,79)(45,81)(46,68)(47,67)(48,69)(49,65)(50,64)(51,66)(52,71)(53,70)(54,72);
s1 := Sym(84)!( 1,37)( 2,39)( 3,38)( 4,43)( 5,45)( 6,44)( 7,40)( 8,42)( 9,41)(10,28)(11,30)(12,29)(13,34)(14,36)(15,35)(16,31)(17,33)(18,32)(19,47)(20,46)(21,48)(22,53)(23,52)(24,54)(25,50)(26,49)(27,51)(55,67)(56,69)(57,68)(58,64)(59,66)(60,65)(61,70)(62,72)(63,71)(73,77)(74,76)(75,78)(79,80);
s2 := 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);
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, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;