Abstract: A beverage container lid includes a round rim and a flange extending beyond the rim. The rim and flange form an outer perimeter having a plurality of local maxima, at least one of which is proximal to a spout, such that the container, when tipped over with the spout oriented downward, will gravitationally roll until the rim rests on one of a plurality of local minima, which in embodiments requires rolling through an angle of no less than 30 degree and/or no more than 90. The local maxima can be equally spaced about the center of the lid and equidistant from the lid center. Between each adjacent pair of local maxima, the perimeter of the lid can be shaped substantially as an arc of a circle, where the circles can have equal radii. In some embodiments the flange extends beyond the rim everywhere.

Abstract: A beverage container lid includes a round rim and a flange extending beyond the rim. The rim and flange form an outer perimeter having a plurality of local maxima, at least one of which is proximal to a spout, such that the container, when tipped over with the spout oriented downward, will gravitationally roll until the rim rests on one of a plurality of local minima, which in embodiments requires rolling through an angle of no less than 30 degree and/or no more than 90. The local maxima can be equally spaced about the center of the lid and equidistant from the lid center. Between each adjacent pair of local maxima, the perimeter of the lid can be shaped substantially as an arc of a circle, where the circles can have equal radii. In some embodiments the flange extends beyond the rim everywhere.

Abstract: A beverage container lid includes a round rim and a flange extending beyond the rim at least proximal to a spout, such that the container, when tipped over with the spout oriented downward, will gravitationally roll until a height of the container's center of mass reaches any of a plurality of local minima. The lid can be configured such that rolling through an angle of no less than 30 degree and/or no more than 90 degrees is required. In some embodiments the flange extends beyond the rim only proximal to the spout, such that the rim contacts an underlying table over a continuous angular range beyond the flange. In other embodiments, the flange extends beyond the rim everywhere, and has a plurality of maximum radii with a plurality of minimum radii interspersed therebetween. In some of these embodiments the flange includes at least one flat, straight line segment.