Abstract: A structured porous metamaterial includes a three-dimensional matrix of at least one repeating base unit. The matrix is formed from an array of at least eight base units, each base unit including a platonic solid including at least one shaped void, wherein each base unit has void geometry tailored to provide a porosity of between 0.3 and 0.97, and to provide the metamaterial with a response that includes a Poisson's ratio of 0 to ?0.5 when under tension and compression, or negative linear compression (NLC), negative area compression (NAC), zero linear compression (ZLC), or zero area compression (ZAC) behaviour when under pressure.