STEREOLOGY FOR SOME CLASSES OF POLYHEDRA

A general method for solving stereological problems for particle syste ms is applied to polyhedron structures. We suggested computing the ker nel function of the respective stereological integral equation by mean s of computer simulation. Two models of random polyhedrons are investi gated. First, regular prisms are considered which are described by the ir size and shape. The size-shape distribution of a stationary and iso tropic spatial ensemble of regular prisms can be estimated from the si ze-shape distribution of the polygons observed in a section plane. Sec ondly, random polyhedrons are constructed as the convex hull of points which are uniformly distributed on surfaces of spheres. It is assumed that the size of the polyhedrons and the number of points (i.e. the n umber of vertices) are random variables. Then the distribution of a sp atially distributed ensemble of polyhedrons is determined by its size- number distribution. The corresponding numerical density of this bivar iate size-number distribution can be stereologically determined from t he estimated numerical density of the bivariate size-number distributi on of the intersection profiles.