Abstract:
This project extends the concept of grationality from regular polygons to regular polyhedra. In two dimensions, grationality arises naturally from area scaling and geometric manipulations. In three dimensions, we introduce structural and arithmetic constraints, since only five regular polyhedra exist and volume scales differently than area. By defining a nice polyhedron as a regular polyhedron with natural-number side lengths, and calling an integer 𝑚 > 3 3D‑Grational when a polyhedron with 𝑚 vertices can be broken into 𝑚 smaller congruent copies, we analyze how these solids behave. These definitions and constraints highlight the fundamental differences between 2D and 3D behavior, reveal new geometric handicaps, and creates conjectures about which vertex counts can support grationality in three dimensions.
Scheduled for: 2026-03-28 10:40 AM: Math... With a Spoon! Session #3 in Computing and Math 355
Status: Accepted
Collection: Math... With a Spoon!
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