This article focuses on the relationship between a lexical database and a derivational map, a hierarchical representation of the lexicon that specifies lexical and morphological inheritance by means of graph theory. In order to take steps towards construing a three-dimensional lexicon, this article also puts forward the concept of semantic pole. A semantic pole is a pivot of lexical organization defined as the area of lexical space comprised of the intersection of the lexical areas of one or more derivational paradigms and the major exponents of a semantic prime. This proposal is applied to the semantic pole sōð-trēowe in Old English and two main conclusions are reached. Firstly, a semantic pole constitutes a panchronic representation of lexical relations that contributes to the development of the third-generation Internet, which aims, among other things, at compiling databases and representing contents in 3D. Secondly, the concept of semantic pole constitutes an explanatory principle of derivational morphology and lexical semantics because it explains the degree of convergence between morphological and lexical inheritance, accounts for the clustering of lexical items around certain semantic poles and predicts the rise of polysemy.