Is tactile perception two-dimensional or three-dimensional?
It's not 2D: Tactile perception can very simply understand a ring around your finger. If you projected the skin of your body onto a 2D plane there would be a way to represent this sensation, but only as an irregular shape. So you need a third dimension to cognitively process this sensation.

But Phantom pain tells us the brain doesn't always register tactile perception from a true 3D mapping. For example a person without an arm could feel pain in a finger that doesn't exist. Not always, but sometimes. 

So it's greater than two, and sometimes three doesn't fully describe the known phenomena. Therefore it's (at least) 4-D.