Instead of using powers of the basis to write a number, this system use their factorial!
For example:
$$463_{10}=3\times 5!+4\times 4!+1\times 3!+0\times 2!+1\times 1!+0\times 0!$$
Fun things about these are that
- it is a perfect system to number permutations, and
- the factorial numbers of a given length form a permutohedron.
For more see factorial number system wikipedia page.