Using geometric-combinatorial methods, the complete list of prime alternating links with $n\leq 12$ crossings, is derived. All the links obtained, belonging to the corresponding subworlds and given in Conway notation, are classified in infinite series of links - the families. Combinatorial formula giving the number of rational links for every $n$ is derived, as well as some combinatorial results for the number of polyhedral source links for $n\leq 12$.