That's a good point. High dimensional objects can obtain very unintuitive properties, like you describe. This to me feels similar in many ways to how a corner

That's a good point. High dimensional objects can obtain very unintuitive properties, like you describe. This to me feels similar in many ways to how a corner in a high dimensional n-cube, although 90 degrees, no matter how you measure it, seems extremely spiky. As the shape does not increase in width, but the corners extend arbitrarily far away from the center. A property reserved for spiky things in 3D.