Polyominoid Möbius Bands

A polyominoid is a 3D figure formed by joining squares in the cubic grid edge to edge. A polyominoid band (or loop) is a connected polyominoid in which each cell is joined to two other cells at different edges.

A Möbius Band is a band with only one face. Such a band contains the equivalent of a half-twist, along with any number of whole twists. Thus, either face of any cell can be traced along the band to the opposite face of the same cell. The smallest polyominoid Möbius bands are heptominoids. There are five of them:

Thanks to Karlo Heuer for raising questions about polyominoid structure.

Last revised 2025-07-28.

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Col. George Sicherman [ HOME | MAIL ]