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Objective geometry quality assessment of point clouds is essential to evaluate the performance of a wide range of point cloud-based solutions, such as denoising, simplification, reconstruction, and watermarking. Existing point cloud quality assessment (PCQA) methods dedicate to assigning absolute quality scores to distorted point clouds. Their performance is strongly reliant on the quality and quantity of subjective ground-truth scores for training, which are challenging to gather and have been shown to be imprecise, biased, and inconsistent. Furthermore, the majority of existing objective geometry quality assessment approaches are carried out by full-reference traditional metrics. So far, point-based no-reference geometry-only quality assessment techniques have not yet been investigated. This paper presents PRL-GQA, the first pairwise learning framework for no-reference geometry-only quality assessment of point clouds, to the best of our knowledge. The proposed PRL-GQA framework employs a siamese deep architecture, which takes as input a pair of point clouds and outputs their rank order. Each siamese architecture branch is a geometry quality assessment network (GQANet), which is designed to extract multi-scale quality-aware geometric features and output a quality index for the input point cloud. Then, based on the predicted quality indexes, a pairwise rank learning module is introduced to rank the relative quality of a pair of degraded point clouds.Extensive experiments demonstrate the effectiveness of the proposed PRL-GQA framework. Furthermore, the results also show that the fine-tuned no-reference GQANet performs competitively when compared to existing full-reference geometry quality assessment metrics.