# Touching Planar Polycubes

Touching Planar Polycubes

A planar polycube is a polycube that can be placed in such a way that it extends only one cube high into the third dimension. For each known integer , here are the smallest known planar polycubes such that congruent copies all touch each other.

n

n

This problem area is far from fully analyzed or understood and you might well find better solutions than the ones presented here.