If physical space informs conceptual space, how does it fit in three dimensions?

Barbara Tversky argues that spatial reasoning and the relative representations of physical objects in physical space is the foundation of conceptual thought. But, if the physical space is coded in three dimensions, how can it provide the richness and expressivity for housing concepts? Word embeddings typically span hundreds of dimensions. Perhaps the non-linear distortions associated with perception and motor action are used as high-dimensional building blocks in the constrained space of three dimensions.