Lock and binary key therefor

A key which has a body along which a plurality of projections are arranged, said plurality of projections all being arranged in a common plane and said plurality of projections all having the same vertical height from the body of the key and defining together a profile of the key, wherein the key has a plurality of key elements being arranged along the body of the key, on which key elements said projections are disposed, defining the profile of the key, wherein the key is buildable from said key elements, wherein the key elements are arranged in a central groove of the body of the key, from which each of the key elements has a downwardly oriented element profile and an upwardly oriented element profile, wherein two or four different element profiles can be obtained from each one of key elements by turning the one key element vertically or horizontally so that when the one key element is turned about its vertical axis both the downwardly oriented element profile and the upwardly oriented element profile are reversed, and turning the one key element about its horizontal axis gives the one key element a new upper element profile and a new lower element profile, and wherein each of the key elements has projections for two or four different element profiles.