Ockham algebras with double pseudocomplementation

The variety dpO consists of those algebras (L; boolean AND, boolean OR, f, *, +, 0, 1) with boolean AND, boolean OR binary, f,* + unary and 0, 1 nullary, and where (L; boolean AND, boolean OR, f, 0, 1) is an Ockham algebra and the unary operations f and * commute, f and + commute. We describe completely the structure of the subdirectly irreducible algebras that belong to the subclass dpK(1,1), characterised by the property f(3) = f.