Noble Poly Shapes: An AI-Assisted Interactive Interface for the Enumeration of Noble Polyhedra

Abstract: We describe Noble Poly Shapes, a browser-based graphical interface for exploring, visualizing, and extracting the complete set of noble polyhedra enumerated by Hill [1]. Noble polyhedra are those polyhedra that are simultaneously vertex-transitive and face-transitive; Hill's computer-assisted proof establishes that, aside from the two known infinite families, exactly 146 such polyhedra exist. The accompanying data library, noble-tools-revised [2], contains the enumeration code and a full set of exported models. This document summarizes the relevant definitions and results of that work and describes the respects in which Noble Poly Shapes differs from the original repository: namely, in providing browser-native visualization, interactive exploration of the catalog, and direct extraction of shape and face data, without requiring the user to run the original enumeration software.