On the other half of our planet, Bolt, Eggleton and Gilks had defined what a magic hexagram was (B. Bolt, R. Eggleton and J. Gilks, “The Magic Hexagram,” Mathematical Gazette 75, 141–142, 1991). Here and now, I take up that definition more broadly, and mount the hexagram on a concave polyhedron that tiles space: Escher’s solid, the stellated rhombic dodecahedron, seen also as the invaginated cuboctahedron and as the compound of three flattened octahedra. Its forty-eight faces, read through the star, are the subject of this book. My aim, however, is beyond recreational mathematics: an intuition induced by personal experience tells me that this extraordinary solid has properties that can help symbolically model a system of sieves on solid logical grounds, which can open the way to a more efficient way of thinking about modern-day medical diagnostics, potentially helping achieve higher success with the diagnoses of rare diseases, so often in disguise.