正方形四角四城

最优不是直接连边或“十字”，而是 Steiner 最小树：

• 在正方形内部引入 2 个 Steiner 点；
• 每个 Steiner 点连接两座相邻城镇，并且两个 Steiner 点之间也相连；
• 在 Steiner 点处三条道路两两夹角均为 $120^\circ$。

该网络呈对称的“双 Y”形结构，且比沿边连接（总长 $3s$）更短（其中 $s$ 为正方形边长）。

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英文解析

The optimal solution is not a direct edge or a "cross," but rather a Steiner minimal tree:

• Introduce 2 Steiner points inside the square;
• Each Steiner point connects to two adjacent towns, and the two Steiner points are also connected to each other;
• At each Steiner point, the three roads meet at angles of $120^\circ$ to each other.

This network forms a symmetric "double Y" structure and is shorter than connecting along the edges (total length $3s$, where $s$is the side length of the square).