Yes, thoughts do have a three dimensional geometric component and when language based thinking is transcended one of the ways of carrying logical sequential thought is by a transforming series of geometric forms. I speculate that that would be a simple best fit abstract on the actual 3D activation of neurones, areas, and synapses associated with particular concepts or nouns, etc.

People who have not experienced more subtle forms of thought feel free to deny the existence of rational thought operating below the level of constructed verbal language. The trouble is that those kind of languages are so complex to decode that the brain has little attention and energy left for the thought itself, and is busy fighting with grammar and spelling and homonyms and homophones, and correspondences in other languages etc etc, instead of attending to the important matters, like what is reality, who am I, what is truth etc. The bigger the vocab, the greater the intelligence, the wider the experiences of life, the bigger the problem, as possibilities expand exponentially. All must be sorted, filtered, tested, and then selected in real time at the speed of normal thought. An astounding feat of biological programming in itself.

If you have ever experimented with meditation or LSD you may have had some of these experiences.

Leaving the level of ordered verbal thinking is a little scary as so many things like sense of self, personal history, description of the 'real' world and one's place in it and relations to it, body consciousness, and so forth are structured in language at the everyday level and fear is associated with 'losing all those things permanently. Of course one soon realizes that inner self is independent of body sense, real world perception data, personal history etc, and that one is essentially a thinking entity in a void. But I go too fast......