Learning from 3D meshes is challenging because the data reside on non-Euclidean surfaces embedded in 3D space. This is particularly evident in domains such as brain cortical surface analysis, where existing models typically rely on ROI-agnostic, face-based, or fixed-size patches. Such patches can duplicate boundary vertices, conflate anatomically distinct regions, or incorporate non-cortical vertices such as those of the medial wall. We develop variable-size supervertex (vSV) partitioning, which groups cortical surface vertices into vSV patches similar to superpixels in images. Building on these vSVs, we design Variable-size SuperVertex Vision Transformer (vSV-ViT), a Vision Transformer that processes vSVs through padding, mask-aware patch embedding, and vertex position embedding. We demonstrate the benefits of the proposed framework through a quantitative analysis of vertex assignment in surface partitioning and downstream tasks using Alzheimer's disease brain image datasets. For downstream tasks, we use meshes of cortical thickness and cortical curvature as input to various encoder models and evaluate classification performance. The superior predictive accuracy of vSV-ViT over recent surface-based models supports its effectiveness for cortical surface learning, with AD-related and sex prediction serving as downstream validation. Extending the framework to other cortical surface applications and broader 3D mesh domains remains future work. Code is available at https://github.com/labhai/vSV-ViT.

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