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Precise seizure identification plays a vital role in understanding cortical connectivity and informing treatment decisions. Yet, the manual diagnostic methods for epileptic seizures are both labor-intensive and highly specialized. In this study, we propose a Hyperdimensional Computing (HDC) classifier for accurate and efficient multi-type seizure classification. Despite previous seizure analysis efforts using HDC being limited to binary detection (seizure or no seizure), our work breaks new ground by utilizing HDC to classify seizures into multiple distinct types. HDC offers significant advantages, such as lower memory requirements, a reduced hardware footprint for wearable devices, and decreased computational complexity. Due to these attributes, HDC can be an alternative to traditional machine learning methods, making it a practical and efficient solution, particularly in resource-limited scenarios or applications involving wearable devices. We evaluated the proposed technique on the latest version of TUH EEG Seizure Corpus (TUSZ) dataset and the evaluation result demonstrate noteworthy performance, achieving a weighted F1 score of 94.6%. This outcome is in line with, or even exceeds, the performance achieved by the state-ofthe-art traditional machine learning methods.