Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,2,9,4}

Atlas Canonical Name {2,2,9,4}*576

Overview

Group
SmallGroup(576,8262)
Rank
5
Schläfli Type
{2,2,9,4}
Vertices, edges, …
2, 2, 18, 36, 8
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

2-fold

3-fold

4-fold

6-fold

12-fold

Covers minimal covers in bold

2-fold

3-fold

Representations

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