Abstract: A polygonal lid and container base provide secure and reliable engagement therebetween, while also facilitating removal of the lid without disturbing contents and without applying undue stress to the lid. The lid includes at least one graspable member near or at a designated “release” vertex that facilitates disengagement of the lid from the container base at the release vertex. The lid further includes regions of enhanced engagement that enhance the attachment of the lid to the container base at least along the two sides of the lid that adjoin the release vertex, causing the overall attachment to be less dependent on attachment at the release vertex. As a result, the strength of attachment at the release vertex can be made weaker than at the other vertices, for easy release of the release vertex, without undue weakening of the overall attachment of the lid to the container base.