Is it illegal to cut a penny in half?

Most countries have a law that makes illegal to deliberately damage or alter a coin.

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Is it illegal to damage or deface coins?

Section 331 of Title 18 of the United States code provides criminal penalties for anyone who "fraudulently alters, defaces, mutilates impairs, diminishes, falsifies, scales, or lightens any of the coins coined at the Mints of the United States." This statute means that you may be violating the law if you change the appearance of the coin and fraudulently represent it to be other than the altered coin that it is. As a matter of policy, the U.S. Mint does not promote coloring, plating or altering U.S. coinage: however, there are no sanctions against such activity absent fraudulent intent.