The observed form of coated vesicles and a mathematical covering problem.

A connection is made between (1) the observed structures of clathrin cages and (2) the mathematical problem of determination of the smallest diameter of n equal circles by which the surface of a sphere can be covered without gaps. For different numbers n of circles, it is found that the various clathrin polyhedra identified so far provide topologically the same configurations as the proven solutions of the sphere-covering problem for some n or improve on the currently best conjectured solutions for other n. Thus a study of some biological structures has, in this case, given additional insight into a mathematical problem.