SOLIDGEO: Measuring Multimodal Spatial Math Reasoning in Solid Geometry

TL;DR

SolidGeo is a comprehensive benchmark designed to evaluate multimodal large language models on complex solid geometry reasoning tasks, revealing significant performance gaps and providing insights into their spatial reasoning capabilities.

Contribution

This paper introduces SolidGeo, the first large-scale benchmark specifically targeting solid geometry reasoning in multimodal models, filling a critical gap in existing mathematical evaluation tools.

Findings

MLLMs perform significantly worse than humans on SolidGeo tasks.

Analysis reveals specific error patterns and inference inefficiencies in MLLMs.

SolidGeo covers diverse 3D reasoning topics, challenging current models.

Abstract

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 efficiency 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.