SolidGeo: Measuring Multimodal Spatial Math Reasoning in Solid Geometry

Geometry is a fundamental branch of mathematics and plays a crucial role in evaluating the reasoning capabilities of multimodal large language models (MLLMs). However, existing multimodal mathematics benchmarks mainly focus on plane geometry and largely ignore solid geometry, which requires spatial reasoning and is more challenging than plane geometry. To address this critical gap, we introduce SolidGeo, the first large-scale benchmark specifically designed to evaluate the performance of MLLMs on mathematical reasoning tasks in solid geometry. SolidGeo consists of 3, 113 real-world K–12 and competition-level problems, each paired with visual context and annotated with difficulty levels and fine-grained solid geometry categories. Our benchmark covers a wide range of 3D reasoning subjects such as projection, unfolding, spatial measurement, and spatial vector, offering a rigorous testbed for assessing solid geometry. Through extensive experiments, we observe that MLLMs encounter substantial challenges in solid geometry math tasks, with a considerable performance gap relative to human capabilities on SolidGeo. Moreover, we analyze the performance, inference effiency and error patterns of various models, offering insights into the solid geometric mathematical reasoning capabilities of MLLMs. We hope SolidGeo serves as a catalyst for advancing MLLMs toward deeper geometric reasoning and spatial intelligence. The dataset is released at https: //huggingface. co/datasets/HarryYancy/SolidGeo/

Authors

• Peijie Wang
• Chao Yang Hunan University
• Zhong-Zhi Li
• Fei Yin National Laboratory of Pattern Recognition (NLPR), Institute of Automation of Chinese Academy of Sciences, Beijing 100190, China School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing 100049, China
• Dekang Ran
• Mi Tian TAL Education Group
• Zhilong Ji Tomorrow Advancing Life
• Jinfeng Bai Tomorrow Advancing Life
• Cheng-Lin Liu School of Artificial Intelligence, University of Chinese Academy of Sciences, State Key Laboratory of Multimodal Artificial Intelligence Systems (MAIS), Institution of Automation, Chinese Academy of Sciences

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