Certifying the robustness of neural networks against adversarial attacks is critical to their reliable adoption in real-world systems including autonomous driving and medical diagnosis. Unfortunately, state-of-the-art verifiers either do not scale to larger networks or are too imprecise to prove robustness, which limits their practical adoption. In this work, we introduce GPUPoly, a scalable verifier that can prove the robustness of significantly larger deep neural networks than possible with prior work. The key insight behind GPUPoly is the design of custom, sound polyhedra algorithms for neural network verification on a GPU. Our algorithms leverage the available GPU parallelism and the inherent sparsity of the underlying verification task. GPUPoly scales to very large networks: for example, it can prove the robustness of a 1M neuron, 34-layer deep residual network in $\approx$ 22 seconds. We believe GPUPoly is a promising step towards the practical verification of large real-world networks.