Your image of extruding a cylinder in higher dimensions inside its bounding box then rounding it off was really insightful as a teaching tool. I've always struggled to visualize these "counterintuitive" results, which are only counterintuitive because they are harder to visualize or seem to "change" after D=3. But now they don't. Thanks!
Hypercubist Math has the ambitious goal of imbuing an intuitive sense of 4-dimensions to people. Currently at Vol. 2 of a several-volume series, will be interssting whether they succeed or not if user feedback is anything to go by.
