From Phys.org:
The periodic table of elements that most chemistry books depict is only one special case. This tabular overview of the chemical elements, which goes back to Dmitri Mendeleev and Lothar Meyer and the approaches of other chemists to organize the elements, involve different forms of representation of a hidden structure of the chemical elements. This is the conclusion reached by researchers at the Max Planck Institute for Mathematics in the Sciences in Leipzig and the University of Leipzig in a recent paper. The mathematical approach of the Leipzig scientists is very general and can provide many different periodic systems depending on the principle of order and classification—not only for chemistry, but also for many other fields of knowledge.
It is an icon of natural science and hangs in most chemistry classrooms: the periodic table of elements, which is celebrating its 150th birthday this year. The tabular overview is closely linked to Dmitri Mendeleev and Lothar Meyer—two researchers who, in the 1860s, created an arrangement of elements based on their atomic masses and similarities.
More here. [Thanks to Farrukh Azfar.]