Polytope of Type {6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6}*1944g
if this polytope has a name.
Group : SmallGroup(1944,2344)
Rank : 3
Schlafli Type : {6,6}
Number of vertices, edges, etc : 162, 486, 162
Order of s₀s₁s₂ : 18
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {6,6}*648a, {6,6}*648g
   6-fold quotients : {6,6}*324b
   9-fold quotients : {6,6}*216b, {6,6}*216d
   18-fold quotients : {6,6}*108
   27-fold quotients : {6,6}*72a, {6,6}*72b, {6,6}*72c
   54-fold quotients : {3,6}*36, {6,3}*36
   81-fold quotients : {2,6}*24, {6,2}*24
   162-fold quotients : {2,3}*12, {3,2}*12
   243-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*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*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*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*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1 >;

References : None.
to this polytope