The periodic table is like anything in science - it changes with new information. We've added new elements and the original organization by Mendeleev was based on atomic mass, not atomic number (Henry Mosely did the reorganization for that piece). However, with more and more information about elements being found, such as orbitals and quantum numbers, other variations of the basic periodic table can be found. I'm not talking about those "Periodic Table of the Vegetables" posters you see around, but rather a real reorganization of the elements that includes or is based around a different property than simply the atomic number. These alternative versions are not widely used, but they are definitely cool to look at. Here are a few examples:
This is the table designed by Professor Theodor Benfey in 1960

This one is by Mohammed Abubakr

The Najderek table emphasizes the energy levels and orbitals nicely:

The Physicists table adds in quantum numbers:

This one is just sorta weird - but pretty!

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