Playing with Inkscape and rotating an ellipse I came up with this:
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Nice! Love those accidental “Eureka” moments! 
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That’s pretty damned cool.
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Playing with the idea some more…
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And still smaller the lines are too thin to cut out but not too thin to engrave.
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A Fine wandering though a program results in a highly re-purposeful design. Many from one.
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This design would also make a nifty guitar pick. I’m not sure what material to use for that, though. Acrylic, I think, might prove to be to brittle and inflexible.
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Natural turtle shell I think if available from a legal source. I had some manufacturing scrap back in 1975ish that was probably 20 years old then from an estate of an old jeweler that you might have managed that, but I don’t know if you can even posses it now… The plastic that emulates it sold these days, would be interesting to look at but I would have no idea of the chemistry of that plastic.
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