Part of the Atlas of Small Regular Polytopes

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

Atlas Canonical Name {4,2,4,9}*1152

Overview

Group
SmallGroup(1152,155402)
Rank
5
Schläfli Type
{4,2,4,9}
Vertices, edges, …
4, 4, 8, 36, 18
Order of s0s1s2s3s4
36
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

8-fold

12-fold

24-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := ( 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)(39,76)(40,75);;
s3 := ( 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);;
s4 := ( 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);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(76)!(2,3);
s1 := Sym(76)!(1,2)(3,4);
s2 := Sym(76)!( 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)(39,76)(40,75);
s3 := 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);
s4 := 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);
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*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, s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;