LatticeData[]

LatticeData["Properties"]

vv=LatticeData["BodyCenteredCubic", "Image"]

LatticeData["FaceCenteredCubic", "Image"]

WSFCC=PolyhedronData["RhombicDodecahedron","Faces"];

Show[Graphics3D[{ Opacity[.2],WSFCC}]]

WSBCC=PolyhedronData["TruncatedOctahedron","Faces"];

Show[Graphics3D[{ Opacity[.2],WSBCC}]]

b=LatticeData["BodyCenteredCubic","Basis"]

l1=Flatten[Table[i b[[1]]+j b[[2]]+k b[[3]],{i,0,3},{j,0,3},{k,0,3}],2];

Graphics3D[Map[Sphere[#,.2]&,l1],Boxed->True,Axes->True]

HL=LatticeData["SimpleHexagonal","Image" ];

Show[HL]

HCP=LatticeData["HexagonalClosePacking","Image" ];

Show[HCP]

DIA=LatticeData["TetrahedralPacking","Image"]