Construction of a Tetrahedron Packing Model: A Puzzle in Structural Chemistry

In the introductory chemistry course, the molecular structure of matter is perhaps one of the most important con- cepts. The use of models to explain the arrangement of atoms and molecules in solids has been widely discussed,l-* and the construction of cubic arrays is a popular laboratory exerc i~e .~ This paper proposes the assembly of a tetrahe- drally shaped packing model as a game or puzzle for students, generating interest and enthusiasm while impressing on them the order and symmetry of solids.

The model is constructed of spheres of suitable material and size. For example, we used expanded polystyrene spheres 4.5 cm in diameter. Two different units (Fig. 1) are used as building blocks, two of each type being assembled in advance. The problem posed to the students is to arrange these four arrays of spheres in such a way as to form a tetrahedron (Fig. 2).

Many students immediately abject that the pieces, which can he easily stacked to farm a cubic array, cannot pos- sibly farm a tetrahedron with its obvious threefold symmetry. It is of benefit to first display the assembled tetrahe- dron, then quickly disassemble it into its components in order to demonstrate the feasibility of solution. The mare as- tute student may note that the tetrahedron has four spheres on an edge and begin his construction with the unit of four spheres in line (Fig. l (a)) . The solution is shown in Figure 3.

Figure 1. Two different arrays of spheres used to assemble the tetrahedron.

Figure 2. The assembled tetrahedral model.

Figure 3. Arrangement of the four arrays of spheres to form a tetrahedron.

The exercise described is the reverse of the traditional demonstration of cubic symmetry in the stacking of hexag- onal and triangular two-dimensional arrays of spheres.' A desk model af the assembled tetrahedron may have colored spheres to indicate hexagonal packing and symmetry within the model. This may be used as a departure point for a further discussion of packing and symmetry and the building of appropriate models.

Northfield Mount Herman School Mt. Hermon, Massachusetts 01354

William W. Sehweikert

Volume 52, Number 8, August 1975 / 501