Dan Asimov <dasimov@earthlink.net> wrote:

At this point, I'm pretty sure *what* I think is the number one distinction between the extremes of the regular simplex and the sphere, though I haven't yet convinced myself I know exactly *why* I believe this.

Meanwhile, if anyone else would like to express their opinion, I'd be curious to learn what others think about this.

The simplex is sharper, hence more likely to hurt your hand when you pick it up. The sphere is rounder, hence more likely to roll away and fall off the table when you set it down. I'm not sure I understand your question. :-) The simplex is best at being best at being self-dual. (Except in 2 dimensions where every regular polygon is self-dual.) I think it's the most rigid solid even if the edges are linked by hinges.