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The properties of architected materials are governed largely by their structural connectivity, suggesting that the ability to reconfigure their architecture provides a powerful means of tuning their properties. However, as structural connectivity is fixed during printing, existing routes to reconfigurability have had to rely on connectivity-preserving mechanisms such as buckling or rotation, or on transient pseudo-connections that persist only under certain conditions. Here, we introduce a codesign strategy in which dynamic self-healing polymers and architecture are engineered together to make connectivity a programmable design variable. We develop vat photopolymerization–compatible polymer networks bearing dynamic boronate ester crosslinks that allow discrete structural elements to self-heal, and thus weld, on contact under ambient conditions. Positioning two initially disconnected beams into contact for a defined period triggers reversible bond exchange and forms a new mechanical connection, allowing reversible modification of structural connectivity post-fabrication. Using this strategy, we program increasingly complex mechanical responses within 3D printed structures: on-demand stiffening through a single weld, transitions from bending- to stretching-dominated deformation via selective welding and even toggling of auxetic behavior. Overall, this work establishes dynamic covalent networks as a general strategy for reconfigurable connectivity-changing architected materials with adaptable and tunable mechanical functionality.