Add to ORKGThe present work studies the mechanical response of confined pentamode lattices equipped with rigid connections, with the aim of designing innovative extreme materials that show high compression modulus and low shear modulus. Employing a computational design approach, we show that the mechanical response of pentamode lattices with rigid connections is bending-dominated, and that such structures are able to carry unidirectional compressive loads with sufficiently high stiffness, while showing markedly low stiffness against shear loads. Differently from systems equipped with hinged connections, the high ratio between effective compression and shear rigidities stems from the nonzero bending rigidity of nodes and rods, and from the confinement ...