Polyominoid
In geometry, a polyominoid (or minoid for short) is a set of equal squares in 3D space, joined edge to edge at 90- or 180-degree angles. The polyominoids include the polyominoes, which are just the planar polyominoids. The surface of a cube is an example of a "hexominoid," or 6-cell polyominoid, and many other polycubes have polyominoids as their boundaries. Polyominoids appear to have been first proposed by Richard A. Epstein. Classification. 90-degree connections are called "hard"; 180-degree connections are called "soft". This is because, in manufacturing a model of the polyominoid, a hard connection  would be easier to realize than a soft one. Polyominoids may be classified as "hard" if every junction includes a 90° connection, "soft" if every connection is 180°, and "mixed" otherwise, except in the unique case of the monominoid, which has no connections of either kind. The set of soft polyominoids is equal to the set of polyominoes. As with other polyforms, two polyominoids that are mirror images may be distinguished. "One-sided" polyominoids distinguish mirror images; "free" polyominoids do not. Enumeration. The table below enumerates free and one-sided polyominoids of up to 6 cells. Generalization to  higher dimensions. In general one can define an "n,k-polyominoid" as a polyform made by joining "k"-dimensional hypercubes at 90° or 180° angles in "n"-dimensional space, where 1≤"k"≤"n".