An auxetic structure includes a plurality of polyhedral units arranged adjacent one another to form a three-dimensional structure. Each polyhedral unit has protrusions extending orthogonally from some surfaces thereof and recesses formed in other surfaces thereof. The protrusions of each polyhedral unit are slidingly received in corresponding recesses of adjacent polyhedral units. A plurality of sleeves are positioned around each protrusion and in a corresponding recess. The sleeves are formed from a softer material than the protrusions. An auxetic effect is achieved by shear-induced displacement of the protrusions in corresponding recesses.