No. Snowflakes come in different shapes, not just the six-sided star-like shapes that most people think of first. Some are in the shape of needles, hollow columns and even tiny barbells. However, the vast majority of snowflakes are six-sided and symmetrical. These snowflakes form in this way because of how the molecules inside ice line-up and connect to each other.
But remember, these shapes don't always hold up as the flakes fall to earth. Individual crystals often clump together or become damaged, changing their shape as they fall.