Characterization of forbidden particles

While huge amounts of angular comminuted material are mined, manufactured and used yearly, little work on classifying the particle shape of these fragments exists. A quarter of a millennium ago, Euler showed that the sum of a particleʹs Faces (F) and Vertices (V) minus its Edges (E) equals two (F+V−E=2). A decade ago, Meloy developed three additional relationships specific to comminuted brittle material. These additional laws state that if one knows the count of one number, say faces, then one can compute the number of edges and vertices that exist in that particle. For example, if a given normal particle has 10 faces, then the particle will have 15 edges. Sometimes “forbidden particle shapes” arise, as do chiral particle shapes. The problems these shapes cause are discussed in this paper. This work lays a foundation for a practical angular particle characterization system for ballast, comminuted particles and angular particle shapes.