It's often repeated but describing spheres as "spikey" isn't right at all. The argument made is that they seem spikey in rectangular coordinates. But that's act

It's often repeated but describing spheres as "spikey" isn't right at all. The argument made is that they seem spikey in rectangular coordinates. But that's actually a statement about cubes, which are spikey. That's easy to see even just considering 2 and 3 dimensions : the corner of a cube is better for stabbing than a side. But the sphere is rotationally symmetric in all dimensions and is not spikey in the least bit.