The three dimensional polyominoes of minimal area
The three dimensional polyominoes of minimal area
The set of the three dimensional polyominoes of minimal area and of volume $n$ contains a polyomino which is the union of a quasicube $j\times (j+\delta)\times (j+\theta)$, $\delta,\theta\in\{0,1\}$, a quasisquare $l\times (l+\epsilon)$, $\epsilon\in\{0,1\}$, and a bar $k$. This shape is naturally associated to the unique decomposition of $n=j(j+\delta)(j+\theta)+l(l+\epsilon)+k$ as the …