A Tiling instance that represents a valid tessellation is a graph with the following properties:
- all nodes connected to at least 2 other nodes (degree >= 2) - otherwise, a node of degree 0 would represent an external point and a node of degree 1 an open polygon
Invalid since node 4 has degree 1
- all nodes connected to at most 6 other nodes (degree <= 6) - otherwise, a node would have > 6 adjacent polygons (impossible since the polygon with the smaller exterior angle, the regular triangle, fills the full angle with 6 units)
Invalid since node 1 has degree 7
- the graph is connected
Invalid since nodes 1, 2, 3 are not connected to nodes 4, 5, 6
- there exist no adjacent polygons at the same vertex
Invalid due to polygons at node 2
- there exist no adjacent polygons at the same vertex making more than a full circle
Invalid due to three squares and a regular pentagon at node 3 that make more than a full circle
Invalid due to overlapping squares and a regular pentagon at node 3
- there exist no overlapping areas
Invalid due to overlapping area
Invalid due to overlapping area and sides: edges 2~5 with 21~19 and 3~6 with 22~17
- there exist no overlapping sides
Invalid due to the overlapping sides 2~5 and 24~19
- there exist no overlapping vertices
Invalid due to the overlapping vertexes 6 and 15
- there exist no "inside gaps", they would be considered non-regular unit polygons
Invalid due to a gap
