Tightest Arrangements of All Different Nets of a Cube

Summary

Since the 1950’s, polyominoes (that is, shapes consisting of edge-connected unit squares) have gained significant interest both as objects of combinatorial study and as classics of recreational mathematics. There is a very natural collection of such shapes, namely the 11 distinct polyhedral nets of the unit cube. An interesting question is: how tightly can the nets fit together? It is equivalent to search for the smallest perimeter a shape built of them can have. In this article, we provide the exact lower bound as an invitation to study analogous problems for different families of polyominoes.

MSC:

• 52C20

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Notes on contributors

Piotr Pikul

Piotr Pikul (MR Author ID: 1411644, ORCID 0000-0001-7461-0248) defended his Ph.D. thesis at Jagiellonian University on pi day, 2023. While his main research areas are operator theory and general topology, he also writes popular texts on, for example, discrete mathematics or classical geometry.