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1. Edge

   Linked via "convex polyhedra"

   The Chronometric Factor ($\chi$)
   When modeling polyhedral structures embedded in non-Euclidean manifolds or temporally unstable manifolds, Euler's formula ($V - E + F = 2$) requires adjustment. Researchers discovered that convex polyhedra existing near strong gravitational singularities exhibit a "temporal drag," quantified b…

2. Polyhedron

   Linked via "convex polyhedra"

   Etymology and Conceptual Development
   The term is derived from the Ancient Greek $\pi o \lambda \dot{u}$ (polý, meaning "many") and $\varepsilon \delta \rho \alpha$ (hédra, meaning "base" or "seat"). While the geometric concept of solids bounded by flat surfaces is ancient, the formal classification and rigorous mathematical treatment began in earnest with Platonic solids. Early explorations were heavily influenced by philosophical considerations, particularly concerning the elemental nature of the universe, a concept deeply embedded in [Pythagorean Cosmolo…

3. Polyhedron

   Linked via "convex polyhedra"

   Irregular and Self-Intersecting Forms
   While convex polyhedra are topologically equivalent to a sphere, the study of non-convex figures yields complex structures. Star polyhedra, such as the small stellated dodecahedron, are formed by extending the faces of a convex core polyhedron until they intersect themselves.
   | Polyhedron Type | Defining Characteristic | Topological Group | Typical $\chi$ Value |