The GPCRs [1] that do most of our sense signalling are each individually complicated machines.

Many of our signals are "on" and are instead suppressed by detection. Ligand binding, suppression, the signalling cascade, all sorts of encoding, ...

In any case, when all of our senses are integrated, we have rich n-dimensional input.

- stereo vision for depth

- monocular vision optics cues (shading, parallax, etc.)

- proprioception

- vestibular sensing

- binaural hearing

- time

I would not say that we sense in three dimensions. It's much more.

[1] https://en.m.wikipedia.org/wiki/G_protein-coupled_receptor