> But most important, the fractal possesses various counterintuitive mathematical properties. Continue to pluck out ever smaller pieces, and what started off as a cube becomes something else entirely. After infinitely many iterations, the shape’s volume dwindles to zero, while its surface area grows infinitely large.<p>I'm struggling to understand what is counterintuitive here. Am I missing something?<p>Also, it's still (always) going to be in the shape of a cube. And if we are going to argue otherwise, we can do that without invoking infinity—technically it's not a cube after even a single iteration.<p>This feels incredibly sloppy to me.