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mikepound / cubes

This code calculates all the variations of 3D polycubes for any size (time permitting!)
MIT License
163 stars 43 forks source link

You ask for a language which accounts for rotation, but you really want a language that erases both rotation and reflection. #1

Open Kerdek opened 1 year ago

Kerdek commented 1 year ago

You need a language in which writing down any point requires you to also write down every point which could correspond to that under taxicab rotation/reflection. This means every time you write down a point, you also write down eleven other points (in three dimensions). Testing whether any two points are equal is equivalent to a set comparison (the two sets contain all the same points). Testing whether any sets of points are equal extends from this.

There's your maximal language of k-ominoes. Enjoy.

Kerdek commented 1 year ago

Happy to answer any questions.

Kerdek commented 1 year ago

Worth mentioning it doesn't actually matter that the point sets are contiguous. Equivalences of (contiguous) k-ominoes is are special cases of equivalences of point sets.