Hypanthium
Some flowers have a hypanthium, cylindrical or cup-like structure that has the petals, sepals, and stamens attached to its rim. A flower with a hypanthium may have a superior ovary or an inferior ovary.
A hypanthium often is formed from the fused bases of the petals, sepals, and stamens. Sometimes, however, it appears to be made from a cup-like expansion of the receptacle.
Regardless of how a hypanthium is formed, we describe the flowers pictured above as having free petals (i.e., petals not fused to any others) attached to a hypanthium. We also consider the sepals free, but attached to a hypanthium. In other words, when determining whether the floral organs are fused or not in a flower with a hypanthium, we ignore the fact that the hypanthium is often the fused bases of these organs. We just call the hypanthium a separate structure.