It is very difficult for me to see the "slices" of the hypercube as "slices." I guess that's natural.
My favorite slicings are of the cylinder and the cone, because it's so neat to see the diversity of shapes that result when these figures are sliced. The cylinder is especially cool because of the clear progression toward infinity in the parabolic slicings.
The contour maps were harder for me to understand, perhaps because they are less regular and more unwieldy. Representing 3-D info on a 2-D page is a necessary evil if we are to discuss and understand these concepts, I guess. They're frustrating, of course.
Studies of slicing are more dynamic than studies of just shape and structure, because slicing involves movement, tilting, filling and emptying. The fact that the "slices" inside a figure like the doughnut/bagel change as the figure is moved around seem to suggest that they themselves (the slices) are in a kind of different dimension from the figure. Yes, they exist within it, but they can change while it remains constant. In one sense, the slices are of a lower dimension than the figure they exist within, but in another way they possess a dynamism that the more static outer figure lacks. Don't think that proved anything new, but it's kind of neat.
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