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Explore a thought-provoking lecture that challenges fundamental mathematical concepts about regular polytopes and examines the divergence between mathematical and physical reality. Professor N J Wildberger questions the universally accepted notion that exactly five regular (Platonic) solids exist: the tetrahedron, cube, octahedron, icosahedron, and dodecahedron. Begin with an examination of regular polygons in the plane, where the presenter offers a conjecture that contradicts prevailing mathematical dogmas. Discover connections to Rational Trigonometry, which approaches metrical geometry purely algebraically using rational numbers or finite fields, and learn about the properties of "Spread Polynomials." The discussion extends to Ludwig Schlafli's classification of regular solids in higher dimensions, with special attention to remarkable 4D solids, including one that requires creating an extension field containing a "square root of 5." This 26-minute presentation from Insights into Mathematics challenges conventional mathematical thinking and explores the fascinating disconnect between mathematical theory and physical reality.
