Relational information about items in memory is thought to be represented in our brain thanks to an internal comprehensive model, also referred to as a “cognitive map”. In the human neuroimaging literature, two signatures of bi-dimensional cognitive maps have been reported: the grid-like code and the distance-dependent code. While these kinds of representation were previously observed during spatial navigation and, more recently, during processing of perceptual stimuli, it is still an open question whether they also underlie the representation of the most basic items of language: words. Here we taught human participants the meaning of novel words as arbitrary labels for a set of audiovisual objects varying orthogonally in size and sound. The novel words were therefore conceivable as points in a navigable 2D map of meaning. While subjects performed a word comparison task, we recorded their brain activity using functional magnetic resonance imaging (fMRI). By applying a combination of representational similarity and fMRI-adaptation analyses, we found evidence of (i) a grid-like code, in the right postero-medial entorhinal cortex, representing the relative angular positions of words in the word space, and (ii) a distance-dependent code, in medial prefrontal, orbitofrontal, and mid-cingulate cortices, representing the Euclidean distance between words. Additionally, we found evidence that the brain also separately represents the single dimensions of word meaning: their implied size, encoded in visual areas, and their implied sound, in Heschl's gyrus/Insula. These results support the idea that the meaning of words, when they are organized along two dimensions, is represented in the human brain across multiple maps of different dimensionality. Significant statementHow do we represent the meaning of words and perform comparative judgements on them in our brain? According to influential theories, concepts are conceivable as points of an internal map (where distance represents similarity) that, as the physical space, can be mentally navigated. Here we use fMRI to show that when humans compare newly learnt words, they recruit a grid-like and a distance code, the same types of neural codes that, in mammals, represent relations between locations in the environment and support physical navigation between them.