MathLabs

第1题

确定所有 finite sets S S 的在least three 点s 中plane which satisfy following condition: F或any two distinct 点s A A 且 B B 中 S S , perpendicular bisect或的直线 segment AB AB 是an ax是的symmetry 的 S S .
第 4/6 步：Fix 中心
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通俗地说

All symmetries 的hull pass through its 中心.

O is the center of the regular hullO\text{ is the center of the regular hull}
详细分析

Every symmetry ax是的 S S preserves its convex hull 且therefore fixes 中心 O O 的regular polygon. 若 X∈S X\in S were 不a hull vertex, choose a 三角形 OAiAi+1 OA_iA_{i+1} 译文： containing it.