Triangle belong to tile

Tiles are building with triangles. But it is useful to define conditions for a triangle that to be considered part of the tile in order to delimit spatial extension of the graphical pattern.

Definition 3   A triangle $t_n$ belongs to a tile $m_i$ , typed $t_n\in m_i$ , when $m_i$ lost its tile's properties, after that $t_n$ is removed from $m$ .

Essentially tile's properties are two neither holes nor overlaps. But we must add the condition that the cover be composite by legal patches. The first part of these conditions is not complished normally.

Figure 4: Membership of triangle to tile: (a) Tile's triangles $M=<t_4,t_{0_1},t_{0_2},t_1>$ . (b) Full-cover (c) Cover with a patch defined by $M'\leftrightharpoons M-\{t_1\}$