Connor Hill, a 17-year-old student at Delta High School in Pennsylvania, United States, proved the existence of exactly 146 isolated noble polyhedra, revealing 85 new three-dimensional shapes that were totally unknown to the scientific community. The feat closed a mathematical question that had remained open since the 1870s, when German mathematician Edmund Hess began the study of these symmetric geometric figures. The complete proof was published on the academic repository arXiv.
The noble polyhedra are three-dimensional structures of high complexity where all faces and all vertices are exactly identical to each other by symmetry. Until 2020, mathematicians only knew of two infinite families and 61 isolated cases, without certainty of how many more could exist. The challenge lay in the virtually infinite volume of hypotheses to test, which made the search practically impossible with traditional methods.
Connor Hill overcame the barrier by crossing geometry with algebra. He used polynomials to transform an infinite search into a finite set of equations and wrote a computer program to systematically test all remaining possibilities. The process culminated in the discovery of the 85 missing shapes and the mathematical demonstration that no more cases exist to be found. The young man revealed that, at first, he thought he would only find a few new examples.
The feat earned Connor Hill first place in the Regeneron Science Talent Search 2026, considered the most prestigious science competition for secondary school students in the United States, guaranteeing him a prize of $250,000. Beyond resolving a historical question over 150 years old, the methodology developed by the young man could be applied in solving other complex problems in modern geometry.
