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Trying to design mirror shape using hexagonal segments, but can't figure out angle to make them mesh together properly

Question asked by Kevin Hjelstrom on May 10, 2017

I am currently working on making a model of the James Webb Space Telescope, and after designing the mirror segments as perfect hexagons, I realized that they would not mesh together properly when brought up at an angle. How do i figure out the side angles for the hexagons in the first ring around the center, as well as for the ones that will comprise the second ring?


This image shows the overlap at the end of the hexagons that I am trying the solve. The corners should be coincident


This is the side view of the mirror assembly.