Intermetallic Crystal Structures as Foams. Beyond Frank–Kasper

In many intermetallic
structures, the atoms and bonds divide space into tilings by tetrahedra.
The well-known Frank–Kasper phases are examples. The dual tilings
divide space into a tiling by polyhedra that is topologically a foam.
The number of faces of the dual polyhedron corresponds to the atom
coordination number in the direct structure, and face sharing by adjacent
polyhedra corresponds to bonds in the direct structure. A number of
commonly occurring intermetallic crystal structures are shown as their
duals. A major advantage of this alternative mode of depiction is
that coordination of all of the atoms can be seen simultaneously.