Although no worked-out examples are available, it seems a promising line of attack. In the case of the Penrose tiling it is interesting to see that there are no classically straight lines anymore, precisely because of the aperiodicity. In the second case vagueness is a possible way out. As Peter Forrest in his (1995), and Crouse and Skufca in their (2019) defend, the whole idea of a specific representation of a discrete space, e.g., as built up from tiny squares is fundamentally mistaken. If a hodon has a specific form, then one cannot avoid asking questions about parts of a hodon, such as its border, but that does not make sense if hodons are the smallest spatial entities possible. An intermediate position defended in Van Bendegem (1997) is to consider a series of discrete geometries \(G_{i}\), each with a hodon of a particular size, \(h_{i}\), such that \(h_{i}\ne h_{j}\), for \(i\ne j\) and, in addition, there are \(M\) and \(N\) such that \(M \lt h_{i} \lt N\), for all \(i\). One can then apply a supervaluation technique to the series. This means that a statement will be True (False) if it is true (false) in every geometry \(G_{i}\).  In all other cases it is Undecided, i.e., true in some and false in some others. Now if \(A\) is the statement “hodons have size \(\alpha\)” (where \(\alpha\) is a specific number), this will be Undecided, if a corresponds to at least one of the \(h_{i}\). Such an approach however introduces all problems connected with vagueness into the discussion, which is not necessarily an encouraging situation. For this problem too, an original answer can be given from within the framework of graph theory.