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Two Circles, Two Ellipses and Two Hyperellipses Walk Into a Hexagon

This was done in Mathematica 11, using ParametricIPOPTMinimize enter image description here
POSTED BY: Frank Kampas
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The objective function is the apothem of the hexagon, the shortest distance from the center to a face. Minimizing it is equivalent to minimizing the area of the hexagon.
POSTED BY: Frank Kampas

Nicely fits together! Very impressive! What is optimized(minimized/maximed) exactly? Total area? or total circumference? or?
POSTED BY: Sander Huisman
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