Gaps and well-composed objects in the triangular grid

Abstract

© 2019, Springer Nature Switzerland AG. We extend the notion of a gap from the square to the triangular grid, and we propose a possible classification of gaps in this grid. We give four definitions of well-composed objects in the triangular grid by translating the existing definitions of such objects in the square grid. We show that these definitions in the triangular grid are equivalent, as they are in the square grid. We give a formula relating the number of gaps of different types in an object in this grid with the number of boundary cells in the object, as well as three short intuitive proofs of this formula.