# PolyComp: A Polycube-based Benchmark for Compositional 3D Spatial Reasoning in Multimodal Models

arXiv: https://arxiv.org/abs/2608.14741 · HTML: https://mlsanity.com/paper/2608.14741/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 19 of its 24 references that are in the map.
- First posted on arXiv 13 Aug 2026.

## Placed in

- LLM reasoning / [Spatial and embodied reasoning](https://mlsanity.com/lr/spatial-and-embodied-reasoning/)

## Builds on (most cited first, 19 of 19)

- [MMMU: A Massive Multi-discipline Multimodal Understanding and Reasoning Benchmark for Expert AGI](https://mlsanity.com/paper/2311.16502/) (2023)
- [MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contexts](https://mlsanity.com/paper/2310.02255/) (2023)
- [CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoning](https://mlsanity.com/paper/1612.06890/) (2016)
- [MM-Vet: Evaluating Large Multimodal Models for Integrated Capabilities](https://mlsanity.com/paper/2308.02490/) (2023)
- [Are We on the Right Way for Evaluating Large Vision-Language Models?](https://mlsanity.com/paper/2403.20330/) (2024)
- [Cambrian-1: A Fully Open, Vision-Centric Exploration of Multimodal LLMs](https://mlsanity.com/paper/2406.16860/) (2024)
- [Eyes Wide Shut? Exploring the Visual Shortcomings of Multimodal LLMs](https://mlsanity.com/paper/2401.06209/) (2024)
- [Thinking in Space: How Multimodal Large Language Models See, Remember, and Recall Spaces](https://mlsanity.com/paper/2412.14171/) (2024)
- [BLINK: Multimodal Large Language Models Can See but Not Perceive](https://mlsanity.com/paper/2404.12390/) (2024)
- [Winoground: Probing Vision and Language Models for Visio-Linguistic Compositionality](https://mlsanity.com/paper/2204.03162/) (2022)
- [MMMU-Pro: A More Robust Multi-discipline Multimodal Understanding Benchmark](https://mlsanity.com/paper/2409.02813/) (2024)
- [A Corpus for Reasoning About Natural Language Grounded in Photographs](https://mlsanity.com/paper/1811.00491/) (2018)
- [ScanQA: 3D Question Answering for Spatial Scene Understanding](https://mlsanity.com/paper/2112.10482/) (2021)
- [SQA3D: Situated Question Answering in 3D Scenes](https://mlsanity.com/paper/2210.07474/) (2022)
- [Visual Spatial Reasoning](https://mlsanity.com/paper/2205.00363/) (2022)
- [SpatialSense: An Adversarially Crowdsourced Benchmark for Spatial Relation Recognition](https://mlsanity.com/paper/1908.02660/) (2019)
- [SpatialBench: Benchmarking Multimodal Large Language Models for Spatial Cognition](https://mlsanity.com/paper/2511.21471/) (2025)
- [InternSpatial: A Comprehensive Dataset for Spatial Reasoning in Vision-Language Models](https://mlsanity.com/paper/2506.18385/) (2025)
- [iVISPAR -- An Interactive Visual-Spatial Reasoning Benchmark for VLMs](https://mlsanity.com/paper/2502.03214/) (2025)

## Abstract (arXiv)

We introduce PolyComp, a procedurally generated and verified benchmark that stresses visual recognition and compositional spatial reasoning. In each problem, a model must identify which of four options shows a pair of polycube components that can be combined to form a target solid. The benchmark contains 120 problems across four geometry families, and each problem has three different presentation formats using either a single image or multiple images. The random guessing baseline is 25%. Across the three presentations (360 presented problems per model), GPT-5.6 Sol with max effort attains 50.0% accuracy (95% problem-cluster CI 43.3-56.7%) at a mean cost of 0.951 per presented problem, Claude Fable 5 with max effort attains 39.4% (33.1-46.1%) at 0.701, and Gemini 3.1 Pro Preview with thinking level high attains 27.5% (22.8-32.5%), near the 25% random guessing baseline, at 0.350. The observed accuracy spread across geometry families is larger than across presentation formats. We present a problem development and evaluation protocol, cost and token accounting, and release the 120 problems.