Hypanthium

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A hypanthium is a bowl-shaped part of a flower consisting of the bottoms of the sepals, petals, and stamens stuck together. It is present in all members of the Rosaceae; in the rose it is so deep, with such a narrow top, that it looks like an inferior ovary (the ovary in Rosoideae, which consists of numerous carpels, is in fact superior).
In eucalyptus this structure is commonly known as the 'gum nut'.