A Comparison of Two- and Three-Dimensional Size Distributions in a Cellular Material

This investigation concerns the comparison of twoand three-dimensional data obtained on a cellular material. By quantitative micrography techniques and spatial measurements, the cellular structure corresponds most closely with the shape of pentagonal dodecahedra, twelve-faced cells having five edges per face. The cell volumes have a normal distribution. The areal distributions of planar sections for various shapes of polyhedra were taken from existing literature. The measured volume distributions from this study were then applied by numerical computer calculations to create a transformation which carried the distribution of volumes (three-dimensional) to the expected distribution of planar areas (two-dimensional). The results of the expected and measured areal data agreed well for assumed complex polyhedral symmetry such as pentagonal dodecahedra, and unsatisfactorily for spherical symmetry. These results demonstrate that the pentagonal dodecahedron is a measurable prototype of cell in grain shapes.