When chatting to a friend, it became apparent to me that geometry has its wooly areas. This may seem like a claim that is not worthy of interested debate, however I am pleased to say many happy hours were spent that night in the pub arguing the contrary. Scientifically speaking, a vertex is the point where any appropriate combination of rays, segments and lines result in two straight "sides" meeting at one place. This is more commonly known as a corner. Very well you say, where is this wooly area you speak of? When considering a cube, geometrically it has eight 'corners' or vertices, six faces and twelve edges. The edges being the straight lines made where two faces meet and the corners being the points where those lines converge. If we now change our definition of a vertex to mean the points in a geometric shape where two edges meet, the grey areas begin to emerge. A cube is an easy enough example to grasp but the issues arise when we take, for example, a cone. A cone consists of a circular base and one face converging to a point above the base. There are no edges in the cone except the one that makes up the circumference of the base therefore the point at the top does not satisfy the definition of a vertex. What then is it? In the case of a sphere, it is obvious that they do not contain any vertices but have one face that is the surface area of the shape. If this is then transformed into a hemisphere, an edge and an extra face appears, but no vertices. A circle is a neverending line that has no start or end point to define it. This means that it either all satisfies the definition of vertices or none of it does. A circle can also be described as a series of infinitely small straight lines joined together to create it. This would then support the definition of a vertex being where two straight lines or edges converge to a point. You now begin to see my dilemma. There are so many factors that come into play when considering more complex geometric shapes that definitions have to quickly change to follow suit. This is the case with a lot of science, especially on a quantum level. These definitions can be applied to geometric shapes of molecules. We know of Buckminster-fullerene and of its spherical structure. What then would happen if a cone shaped structure came into existence? There would have to be a point at which all of the atoms within the molecule converged to form the one vertex found in the cone from the sides of the face. This seems as though it would be fundamentally impossible, though it is an interesting concept for any curious inorganic chemist. It begs the questions, what limits are there to the geometric shapes of molecules, why are there these limits and can a cone really be described as a proper geometric shape at all? When I find these answers they are sure to be posted.... :)