How to find a point or a plane which is equidistant from n planes in an n-dimension space (emphasis on point equidistant from "n planes")

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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.