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I was just wondering whether there were any names for all "polyomino-like" objects. Preferably, objects in this set would satisfy some basic condition (such as being composed of 'tiles' and the boundaries of said tiles would have nonempty intersection with at least one other tile such that the tiles are distinct and either intersect at exactly one point (the vertex) or along an entire hyper-edge) and would include any shape of tile (including higher-dimensional ones) arranged in the same(?) dimensional ambient space. But, if that is too broad, I will take the largest subset thereof. For example, polyabolos, polyominoes, polyiamonds, polyhexes, and somewhat more distantly polyplets all seem to be essentially the same "thing" in two-dimensional Euclidean space: they are polygons arranged on the plane so that they "touch adjacently". So, what is the generic name for these two-dimensional polyguys? And do we generalize to higher dimensions (such as arranging tetrahedra or rectangular prisms in an analogous fashion in Euclidean 3-space)? Can we do such things on a sphere (yielding the possibility for a twee polyguy composed of digons), or other metrics?

Really, I am interested in how general we can make this and how the naming system goes.

Just a note: I may be using nonstandard terminology and/or could be misunderstanding some of the basic properties of such objects; I only just now discovered them.

Thank you for listening to my rambling!

Update: Ah, I see. "Polyform" is fairly generic. It still seems to be the case that the 'tiles' are implicitly supposed to be 2-dimensional and arranged in Euclidean 2-space (and they mostly seem to be objects composed of only one type of 'tile'), but that is pretty much what I was looking for.

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