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I initially started with 6 separate equations in a hybrid function to plot the hexagon, but then I managed to reduce it to 3 (mistakes are here)

$$y^2=\sqrt{3}\left(x-r\right)^2\ \left\{x<r\right\}$$ $$y^2=\sqrt{3}\left(x+r\right)^2\ \left\{x>-r\right\}$$ $$y^2=r^2$$

All I want to know is if there exists a single equation which plots a regular hexagon about the centre,

and the mistakes I have made with this solution

Since I'm a newbie,a bit of help on how to reword this question to make it more specific would be appreciated.

EDIT: I would like to keep the main focus on the hexagon only, i am not interested in the other regular polygons, for simplicity of the problem and for a more detailed answer

Also answer should be expressed as equation relating y and x, not in polar form or parametric

ruby duby
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  • also can't think of a good tag to support the question, would understand downvotes – ruby duby Aug 01 '16 at 11:27
  • You have to add a "regular" hexagon, maybe? – Piquito Aug 01 '16 at 12:56
  • ofc however this is an OVERsimplified version of their problem, not only is it focused primarily on the hexagon, it is also about a hexagon about its centre also @Piquito i did its already there – ruby duby Aug 01 '16 at 13:02

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