looking at apples in an apple bin the other day, i noticed that some people pack apples(or oranges, or tangerines, anything round) into containers using two different ways: some lay the first layer down as squares, and then put the next layer in on top, making sure that the balls are fitting at the lowest points. some also use hexagonal packing, doing a similar thing. i know that the hexagonal packing in the second dimension is the most compact. is it the same in 3 dimensions? what way goes in higher-dimensions?