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Issue 373: This artwork visualizes the hidden geometry of physical networks from brain wiring to vascular systems revealing that their structure is shaped by more than simple efficiency. While traditional theories assume these networks minimize total wiring length, our work shows that reality is more complex as local branching patterns consistently defy those predictions. By considering the full three-dimensional form of connections, we uncover a surprising link to concepts from theoretical physics, where minimizing surfaces maps onto high-dimensional models. Using this, we can predict distinctive features such as trifurcations and characteristic angles, which closely match real biological and physical networks. Our study also highlights the importance of orthogonal sprouts, which are crucial structures that enhance connectivity and function. In summary, our findings suggest that the architecture of life’s networks is governed by deeper geometric principles than previously thought.