Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1296,2984)
Rank
5
Schläfli Type
{6,6,9,2}
Vertices, edges, …
6, 18, 27, 9, 2
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 := ( 4, 7)( 5, 8)( 6, 9)(13,16)(14,17)(15,18)(22,25)(23,26)(24,27)(31,34)(32,35)(33,36)(40,43)(41,44)(42,45)(49,52)(50,53)(51,54)(58,61)(59,62)(60,63)(67,70)(68,71)(69,72)(76,79)(77,80)(78,81);;
s1 := ( 1, 4)( 2, 5)( 3, 6)(10,22)(11,23)(12,24)(13,19)(14,20)(15,21)(16,25)(17,26)(18,27)(28,31)(29,32)(30,33)(37,49)(38,50)(39,51)(40,46)(41,47)(42,48)(43,52)(44,53)(45,54)(55,58)(56,59)(57,60)(64,76)(65,77)(66,78)(67,73)(68,74)(69,75)(70,79)(71,80)(72,81);;
s2 := ( 1,10)( 2,12)( 3,11)( 4,13)( 5,15)( 6,14)( 7,16)( 8,18)( 9,17)(20,21)(23,24)(26,27)(28,66)(29,65)(30,64)(31,69)(32,68)(33,67)(34,72)(35,71)(36,70)(37,57)(38,56)(39,55)(40,60)(41,59)(42,58)(43,63)(44,62)(45,61)(46,75)(47,74)(48,73)(49,78)(50,77)(51,76)(52,81)(53,80)(54,79);;
s3 := ( 1,28)( 2,30)( 3,29)( 4,31)( 5,33)( 6,32)( 7,34)( 8,36)( 9,35)(10,46)(11,48)(12,47)(13,49)(14,51)(15,50)(16,52)(17,54)(18,53)(19,37)(20,39)(21,38)(22,40)(23,42)(24,41)(25,43)(26,45)(27,44)(55,57)(58,60)(61,63)(64,75)(65,74)(66,73)(67,78)(68,77)(69,76)(70,81)(71,80)(72,79);;
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, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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(83)!( 4, 7)( 5, 8)( 6, 9)(13,16)(14,17)(15,18)(22,25)(23,26)(24,27)(31,34)(32,35)(33,36)(40,43)(41,44)(42,45)(49,52)(50,53)(51,54)(58,61)(59,62)(60,63)(67,70)(68,71)(69,72)(76,79)(77,80)(78,81);
s1 := Sym(83)!( 1, 4)( 2, 5)( 3, 6)(10,22)(11,23)(12,24)(13,19)(14,20)(15,21)(16,25)(17,26)(18,27)(28,31)(29,32)(30,33)(37,49)(38,50)(39,51)(40,46)(41,47)(42,48)(43,52)(44,53)(45,54)(55,58)(56,59)(57,60)(64,76)(65,77)(66,78)(67,73)(68,74)(69,75)(70,79)(71,80)(72,81);
s2 := Sym(83)!( 1,10)( 2,12)( 3,11)( 4,13)( 5,15)( 6,14)( 7,16)( 8,18)( 9,17)(20,21)(23,24)(26,27)(28,66)(29,65)(30,64)(31,69)(32,68)(33,67)(34,72)(35,71)(36,70)(37,57)(38,56)(39,55)(40,60)(41,59)(42,58)(43,63)(44,62)(45,61)(46,75)(47,74)(48,73)(49,78)(50,77)(51,76)(52,81)(53,80)(54,79);
s3 := Sym(83)!( 1,28)( 2,30)( 3,29)( 4,31)( 5,33)( 6,32)( 7,34)( 8,36)( 9,35)(10,46)(11,48)(12,47)(13,49)(14,51)(15,50)(16,52)(17,54)(18,53)(19,37)(20,39)(21,38)(22,40)(23,42)(24,41)(25,43)(26,45)(27,44)(55,57)(58,60)(61,63)(64,75)(65,74)(66,73)(67,78)(68,77)(69,76)(70,81)(71,80)(72,79);
s4 := Sym(83)!(82,83);
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*s2*s0*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, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;