From Conway and Guy’s 1966 question about a uniform tetrahedron to modern demonstrations of monostability via uneven weight, this episode unpacks a surprisingly deep journey. We delve into the idea of an obtuse path that fixes the center of mass in a tiny stable zone, the brutal engineering math that demands a heavy core thousands of times denser than the light shell, and the real-world challenges of making that physics work with carbon fiber frames, tungsten carbide cores, and glue tolerances as tight as a fraction of a gram. We connect the math to spacecraft stability and passive self-righting concepts, reflecting on how geometry and material limits shape what’s physically possible. Along the way we ponder the stark boundary between abstract possibility and the laws of nature—why type II tipping would require densities beyond any known material. A provocative, material-world take on a pure math puzzle.

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