How is a pentagram constructed by connecting the vertices of an underlying pentagon?
Answer
By connecting every second point sequentially.
The construction of the pentagram is achieved by utilizing the five existing vertices of a regular pentagon but deliberately avoiding sequential connections. Instead of drawing lines from vertex 1 to 2, then 2 to 3, and so on (which creates the pentagon itself), the construction mandates skipping one vertex each time. For instance, the lines are drawn by connecting vertex 1 to vertex 3, then 3 to 5, then 5 to 2, 2 to 4, and finally closing the figure by connecting 4 back to 1. This process of linking non-consecutive vertices is mathematically described by the skip factor of 2 in the Schläfli notation {5/2}, resulting in the characteristic star shape.
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