Lexical semantic typology has identified important cross-linguistic generalizations about the variation and commonal-ities in polysemy patterns—how languages package up mean-ings into words. Recent computational research has enabledinvestigation of lexical semantics at a much larger scale, butlittle work has explored lexical typology across semantic do-mains, nor the factors that influence cross-linguistic similari-ties. We present a novel computational framework that quan-tifies semantic affinity, the cross-linguistic similarity of lexicalsemantics for a concept. Our approach defines a common mul-tilingual semantic space that enables a direct comparison of thelexical expression of concepts across languages. We validateour framework against empirical findings on lexical semantictypology at both the concept and domain levels. Our resultsreveal an intricate interaction between semantic domains andextra-linguistic factors, beyond language phylogeny, that co-shape the typology of polysemy across languages.