In chemistry, a cluster is a polycyclic array of atoms that is intermediate in character between a molecule and a solid. The shape of a cluster is based upon a trangular-faced polyhedron, also known as a deltahedron. Using a set of semi-empirical rules devised by K. Wade and extended by M. Mingos known either as Wade's Rules or Polyhedral skeletal electron pair theory it is possible to determine, often unambiguously, the shape of a cluster from its chemical formula. Chemistry (in Greek: χημεία) is the science of matter and its interactions with energy and itself (see physics, biology). ... A molecule is the smallest particle of a pure chemical substance that still retains its chemical composition and properties. ... A solid is a state of matter, characterized by a definite volume and a definite shape (i. ... In mathematics, there are three related meanings of the term polyhedron: in the traditional meaning it is a 3-dimensional polytope, and in a newer meaning that exists alongside the older one it is a bounded or unbounded generalization of a polytope of any dimension. ... The triaugmented triangular prism, a convex deltahedron A deltahedron is a polyhedron where all the faces are equilateral triangles The name arises from the fact that an equilateral triangle is the shape of the Greek majuscule delta (Δ). ...