Rectangle division into shapes and connecting adjacent shapes with non-intersecting lines

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Rectangle is divided into several non-convex shapes. Adjacent shape's centroids are connected with straight lines.

For example (here centroids are approximate):

Could it be that some of those line cross each other?

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+-----+-----+
|     |     |
|  +--+--+  |
|  |     |  |
|  +-----+  |
|  |     |  |
|  +--+--+  |
|     |     |
+-----+-----+