Seventeen-year-old Connor Hill has brought new clarity to a long-running geometry puzzle by identifying the full set of so-called noble polyhedra under his framework. These highly symmetrical 3D shapes can include unusual forms with intersecting faces or edges, as long as every face and vertex shares the same symmetry pattern.
Working from Pennsylvania, Hill turned a question that had lingered for more than a century into a computable classification problem. By converting geometric conditions into algebraic equations, he showed that the search space could be reduced to a finite set. His analysis concludes that, beyond two infinite families, exactly 146 noble polyhedra exist -- 85 more than the 61 shapes previously catalogued by 2020.
The project earned Hill the top prize at the Regeneron Science Talent Search, one of the most prestigious student science competitions in the United States. His 34-page preprint, along with released code and model files, now places the result before the mathematical community for further examination.
Hill's method combined symbolic algebra, numerical testing, and geometric verification using tools such as Python-based libraries and Wolfram Language. The approach reflects a growing trend in modern mathematics: using computation not just to test ideas, but to help complete proofs that once seemed too vast to finish by hand.
As Hill prepares to study computational mathematics at MIT, his work stands as a vivid example of how young researchers can reshape established fields. If confirmed, this classification could influence future research in geometry, algebra, and computer-assisted proof design.
