Metals and alloys have been indispensable for technological progress, which proceeds along with the discovery of new materials. Nevertheless, only a fraction of the possible ternary systems is known. Statistical inference methods are used to study the complexity and regularity of materials properties. Properties originating from atomic-level interactions are accurately described employing a linear regression analysis; properties incorporating microstructural and thermal history require a balance between physical and statistical modelling. In spite of this, there is a remarkable degree of symmetry among all properties. By employing a principal component analysis it is proven that ten essential material properties can be described in a three dimensional space; from which Ashby diagrams constitute a particular case. A surprisingly compact model emerges to design new alloys with required properties.