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Explore the fascinating world of h-vectors and the g-conjecture in this 22-minute video featuring June Huh from the Institute for Advanced Study at Princeton University. Delve into the complexities of shapes in higher dimensions, starting with examples and progressing through triangulation, the icosahedron, and simplexes. Examine Euler's formula and its applications in higher dimensional geometry. Gain insights into the groundbreaking g-conjecture and its implications for mathematical research. Enhance your understanding of advanced geometric concepts through clear explanations and visual representations provided by the renowned Numberphile channel.