PolyComp: A Polycube-based Benchmark for Compositional 3D Spatial Reasoning in Multimodal Models
TL;DR
PolyComp, a procedurally generated and verified benchmark that stresses visual recognition and compositional spatial reasoning, is introduced, and the observed accuracy spread across geometry families is larger than across presentation formats.
Abstract
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.
