The amino acid composition of globular proteins of known tertiary structures is analyzed for the classification of the folding classes of protein structures and for a description of their relationship which can be useful in the determination of the folding type of a protein. For each of the folding classes, an ellipsoid in the multidimensional space was constructed from the 20-D vectors of amino acid composition of its member proteins according to standard analytical geometry methods. From this representation, an ellipsoid-based scheme is then presented for determining the folding type of a protein on the basis of its elliptically scaled radial distances from ellipsoid centroids (rather than the conventional Euclidean distances) in a definitive and analytical manner. Among the 132 basis set proteins from which the ellipsoid representations were derived, locations of their individual vectors give correct assignment of the folding type for 127 proteins; this success rate of 96%, though better than those in previous studies, is established to be the theoretical upper limit only for the basis set proteins. Moreover, the geometrical description of the relationship between amino acid composition and protein folding types derived from this analytical (rather than statistical) method indicates that amino acid composition alone cannot determine the protein folding type in all cases. The high success rate for the basis set proteins nevertheless suggests that the ellipsoid representation and the elliptically scaled distances can be more successful in determining the folding type of a protein from its amino acid composition than other analytical approaches reported previously.