Polytope of Type {3,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,6}*768
Also Known As : {3,6}_(8,0), {3,6}₁₆. if this polytope has another name.
Group : SmallGroup(768,1085833)
Rank : 3
Schlafli Type : {3,6}
Number of vertices, edges, etc : 64, 192, 128
Order of s₀s₁s₂ : 16
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Toroidal
   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) :
   4-fold quotients : {3,6}*192
   16-fold quotients : {3,6}*48
   32-fold quotients : {3,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 3, 4)( 5, 6)( 9,14)(10,13)(11,15)(12,16)(17,22)(18,21)(19,23)(20,24)
(25,26)(31,32)(33,53)(34,54)(35,56)(36,55)(37,49)(38,50)(39,52)(40,51)(41,57)
(42,58)(43,60)(44,59)(45,62)(46,61)(47,63)(48,64);;
s1 := ( 2, 4)( 5,16)( 6,13)( 7,14)( 8,15)(10,12)(17,64)(18,61)(19,62)(20,63)
(21,52)(22,49)(23,50)(24,51)(25,54)(26,55)(27,56)(28,53)(29,60)(30,57)(31,58)
(32,59)(34,36)(37,48)(38,45)(39,46)(40,47)(42,44);;
s2 := ( 1,29)( 2,30)( 3,32)( 4,31)( 5,26)( 6,25)( 7,27)( 8,28)( 9,18)(10,17)
(11,19)(12,20)(13,22)(14,21)(15,23)(16,24)(35,36)(39,40)(41,47)(42,48)(43,46)
(44,45)(51,52)(55,56)(57,63)(58,64)(59,62)(60,61);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope