A complete enumeration of the noble polyhedra
Connor Hill · State College, Pennsylvania
First Place ($250,000) · Regeneron Science Talent Search · 2026
A computational classification of noble polyhedra — polyhedra whose faces are all alike and whose vertices are all alike — completing the enumeration of a family that had never been fully catalogued.
Proved two infinite families of noble polyhedra together with 146 isolated examples.
A classification is a closed question: the answer is a complete list, and completeness is provable. Very few student projects can end with "and there are no others", which is exactly why this one lands.
- Computational enumeration
- Polyhedral symmetry classification
- Proof of two infinite families
- Exhaustive search with a completeness argument
- A finite, provable answer is worth more than an open-ended survey when you can reach one
- Computation used in service of a proof is different from computation used to produce a chart — say which you are doing
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