6. Given a regular dodecagon with side length 1, and a unit circle is drawn with each of its vertices as the center, then the plane is divided into $\qquad$ regions (including the open regions outside) by the dodecagon and the 12 unit circles.
Answer: 62
Difficulty: Medium
Examination: Combinatorial Counting
Analysis: Utilizing symmetry, note that each vertex corresponds to 3 groups of regions not adjacent to other vertices, and 4 groups of regions adjacent to adjacent vertices, plus the central and outer regions, 
resulting in a total of $3 \times 12 + \frac{4 \times 12}{2} + 2 = 62$ regions. As shown in the figure above.
This problem can be approached starting from a regular pentagon,
and similar operations on a regular $n$-sided polygon $(n>4, n \neq 6)$ will produce $5n + 2$ regions.