# SOLIDGEO: Measuring Multimodal Spatial Math Reasoning in Solid Geometry

arXiv: https://arxiv.org/abs/2505.21177 · HTML: https://mlsanity.com/paper/2505.21177/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 May 2025.

## Built on by (most cited first, 18 of 18)

- [Euclid's Gift: Enhancing Spatial Perception and Reasoning in Vision-Language Models via Geometric Surrogate Tasks](https://mlsanity.com/paper/2509.24473/) (2025)
- [Geoint-R1: Formalizing Multimodal Geometric Reasoning with Dynamic Auxiliary Constructions](https://mlsanity.com/paper/2508.03173/) (2025)
- [From Narrow to Panoramic Vision: Attention-Guided Cold-Start Reshapes Multimodal Reasoning](https://mlsanity.com/paper/2603.03825/) (2026)
- [StructVRM: Aligning Multimodal Reasoning with Structured and Verifiable Reward Models](https://mlsanity.com/paper/2508.05383/) (2025)
- [GeoLaux: A Benchmark for Evaluating MLLMs' Geometry Performance on Long-Step Problems Requiring Auxiliary Lines](https://mlsanity.com/paper/2508.06226/) (2025)
- [GGBench: A Geometric Generative Reasoning Benchmark for Unified Multimodal Models](https://mlsanity.com/paper/2511.11134/) (2025)
- [Do MLLMs Really Understand Space? A Mathematical Reasoning Evaluation](https://mlsanity.com/paper/2602.11635/) (2026)
- [TangramPuzzle: Evaluating Multimodal Large Language Models with Compositional Spatial Reasoning](https://mlsanity.com/paper/2601.16520/) (2026)
- [How RL Unlocks the Aha Moment in Geometric Interleaved Reasoning](https://mlsanity.com/paper/2603.01070/) (2026)
- [Hilbert-Geo: Solving Solid Geometric Problems by Neural-Symbolic Reasoning](https://mlsanity.com/paper/2605.16385/) (2026)
- [DynaSolidGeo: A Dynamic Benchmark for Genuine Spatial Mathematical Reasoning of VLMs in Solid Geometry](https://mlsanity.com/paper/2510.22340/) (2025)
- [Geoparsing: Diagram Parsing for Plane and Solid Geometry with a Unified Formal Language](https://mlsanity.com/paper/2604.11600/) (2026)
- [PAGER: Bridging the Semantic-Execution Gap in Point-Precise Geometric GUI Control](https://mlsanity.com/paper/2605.15963/) (2026)
- [LatentGeo: Learnable Auxiliary Constructions in Latent Space for Multimodal Geometric Reasoning](https://mlsanity.com/paper/2603.12166/) (2026)
- [Draw2Think: Harnessing Geometry Reasoning through Constraint Engine Interaction](https://mlsanity.com/paper/2605.20743/) (2026)
- [BiNSGPS: Geometry Problem Solving via Bidirectional Neuro-Symbolic Interaction](https://mlsanity.com/paper/2606.04648/) (2026)
- [Dense Neuro-Symbolic Reasoning in a Unified Geometry State](https://mlsanity.com/paper/2610.04280/) (2026)
- [CVIF: A Criticality-Driven Visual Intervention Framework for Geometric Diagram Understanding in MLLMs](https://mlsanity.com/paper/2610.06399/) (2026)

## Abstract (arXiv)

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.