Cup lid with roll and spill limiting rim

A container assembly comprising:

• a beverage container having a substantially round container lip and a container wall extending downward therefrom to a substantially round container base;
• and
• a lid compatible for attachment to said beverage container so as to form therewith a container assembly, the lid comprising:
• a substantially round rim having a substantially uniform radius as measured from a center of the lid, the rim being configured for secure attachment to the container lip;
• a central lid portion surrounded and bounded by the rim;
• a spout extending upward from the central lid portion proximal to the rim, the spout being configured for consumption therethrough of a beverage;
• and
• a flange extending outward beyond an outer edge of the rim;
• a perimeter of the lid being formed by outer edges of the rim and/or the flange, such that when the container assembly is tipped over onto a horizontal surface, the container assembly is supported by a lowest point of the base and by at least one point on the perimeter of the lid;
• wherein a radius of the perimeter of the lid, measured as a function of angular orientation about the center of the lid, includes a plurality of local minimum radii terminating at minimum points and a plurality of local maximum radii terminating at a plurality of maximum points;
• and
• wherein a first of the local maximum radii terminating at a first of the maximum points passes through the spout, such that when the container assembly is tipped over and when the first maximum point momentarily contacts the horizontal surface, the container is gravitationally induced to roll through an angle of no more than 90 degrees until it assumes an orientation in which a height of its center of gravity is at a local minimum.