Help with Triangulating a hexagonal surface pattern to a list of offset points

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I have a surface with a hexagonal pattern. I need to connect, with a line, each of the six vertices to a offset center point. I am having a hard visualizing how I’m going to associate each set of vertices with the offset center points. Everything I have tried so far has resulted in a mess. I mocked up in rhino what I wanted the end result to be for clarity. Any help is appreciated. Thanks.