This study analyses a set of highly English-specific on-constructions of the form [on + NPPLACE], such as: on the bank of the river, (a house) on the beach, on an island, on the plains, on the street, on a farm. The analysis is conducted in the Natural Semantic Metalanguage (NSM) framework originated by Anna Wierzbicka. Six semantically discrete construction types are identified and each is assigned a semantic schema framed in the metalanguage of semantic primes. All of them, it is argued, include a semantic component involving "laterality" (semantic prime SIDE), often in combination with a component involving visibility (SEE). These constructions, along with others, constitute a complex network of grammatical polysemy in English.