Coherence and integrity are properties of such volumes. It is through such properties that significance can be attributed. Enclosure of volumes Volumes are defined by systematically constraining areas in relation to one another, accepting the necessary degree of conceptual discontinuity between the areas of common concern. The areas must be constrained so as to enclose a volume. Thus a 2x2 matrix of categories might be folded into a tetrahedron, a 3x2 matrix could be folded into a cube.
Minimal discontinuity occurs when the volume approximates to a sphere.
Here the challenge is to interrelate the many necessary areas required for such a structure Maximal discontinuity occurs with a minimum number of areas . Here the challenge is to constrain the areas, given the high degree of discontinuity. A regular polyhedron is a more idealistic structure and presupposes that all areas are of the same pattern. With an irregular polyhedron, areas may be of many patterns. As the number of patterns diminishes, the polyhedron approximates more to an ideal structure.