Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,4,9}

Atlas Canonical Name {2,4,9}*288

Overview

Group
SmallGroup(288,835)
Rank
4
Schläfli Type
{2,4,9}
Vertices, edges, …
2, 8, 36, 18
Order of s0s1s2s3
18
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

3-fold

4-fold

6-fold

12-fold

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-fold

Representations

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