WOLFRAM|DEMONSTRATIONS PROJECT

Touching Planar Polycubes

polycube

1

problem a

cubes per tile:

2

tiles displayed:

4

of

4





























tiles displayed

tile opacity

floor

floor grid

floor opacity

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

n

, here are the smallest known planar polycubes such that

n

congruent copies all touch each other.

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