Though their crystalline structure may manifest in a variety of unique shapes and patterns, all snowflakes have six sides. Because the molecules that build up to form a snowflake are made of water, these molecules fit together in a specific and predictable way that will always result in a six-sided crystal. Water molecules may occasionally form 12-sided ice crystals, but this multiple of six is the only known exception to the six-side rule, according to NPR.org.
Though it's said that no two snowflakes are alike, this is a false truism from the perspective that all snowflakes have six sides. In this way, all snowflakes are actually very much alike, though the way each individual snowflake's crystalline structure manifests will be somewhat different from all others. Snowflakes build up bit by bit in a process of freezing water molecules gathering together around strongly negative and positive charged particles, leading to the growth of a three-dimensional, six-sided flake. Changes in atmospheric temperature and humidity as the snowflake moves through the sky toward the ground lead to the unique appearance of each snowflake, but on the molecular level, a predictable set of factors determine how many sides the snowflake will have.