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I am working on an optimization problem where I have converted the physical system into a set of bounding hyperplanes. To keep it simple, let's say I have three planes in $R^3$. I am trying to find the equation of a point or a plane that is equidistant from the three planes.

A couple of resources that I referred to online describe geometric median and Weiszfeld to be helpful in this context. Still, they all describe an equidistant point from multidimensional points and not multidimensional planes.

Nisharg
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  • The points at, say, distance one from a given plane themselves form a plane parallel to the given plane, so you just need to find the equations of those three parallel planes and then solve three linear equations in three unknowns. But this is not a question of math research, which is what this website is intended to handle. – Gerry Myerson Feb 09 '23 at 22:14
  • Thank you for the response, Gerry. I am incredibly sorry; I wasn't sure about this not being the right place to ask this question. – Nisharg Feb 10 '23 at 21:58

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