PUMaC 2025 · 团队赛 · 第 14 题

PUMaC 2025 — Team Round — Problem 14

A 24-cell is a region that can be formed by the following procedure: taking convex hull of 8 vertices formed by permuting integer coordinates ( ± 1 , 0 , 0 , 0) and 16 vertices at all half-integer coordinates ( ± 1 / 2 , ± 1 / 2 , ± 1 / 2 , ± 1 / 2). If we rotate and scale the 24-cell so that each coordinate has absolute value at most 1 in such a way that the 24-cell has greatest hypervolume, how many vertices ( x, y, z, w ) of the 24-cell satisfy x = 1?

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