Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,9,6,6}

Atlas Canonical Name {2,9,6,6}*1296b

Overview

Group
SmallGroup(1296,2984)
Rank
5
Schläfli Type
{2,9,6,6}
Vertices, edges, …
2, 9, 27, 18, 6
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

6-fold

9-fold

18-fold

27-fold

Covers minimal covers in bold

None in this atlas.

Representations

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