Motivation - Our objective was to design a Boolean algebra allowing both a diagrammatic and sentential representation of logical propositions in an intuitive manner. The purpose of this notation is to support inferential activity without heavy deductive procedure to follow. Research approach - This research is founded on the notions of logical space proposed by Wittgenstein and of hypercube proposed by Pólya. Findings/Design - Complex propositions in propositional logic can be depicted by hypercube within a coordinate system, and by sequences of lexical symbols allowing operations on hypercube with more than three dimensions. Research limitations/Implications - Empirical studies are now required to validate the intuitiveness of this notation. Its scope of application must also be delimited. Originality/Value - Contrary to classical diagrammatic notations based on Euler topological diagrams in logic, the hypercube algebra involves a coordinate-based representation combining diagrams and lexical symbols. This is a new form of notation. Take away message - Rather than the format, the important variables in designing a representational system are those specifying the cognitive activity induced, e.g. straightforward inferences, abstraction level of symbols.