Cognitive approach to analysis of regular packing of congruent objects on plane

Abstract

New approach to investigate the two-dimensional regular packing of arbitrary geometric objects (GOs) using cognitive visualization is presented. GO correspond to congruent non-convex polygons with their associated coordinate system. The origins of these coordinate systems are accepted by object poles. The approach considered is based on cognitive processes that are forms of heuristic judgments. According to the first heuristic judgment, regular packing of congruent GOs on the plane have a honeycomb structure, that is, each GO contacts six neighboring GO, the poles of which are vertices of the pole hexagon in honeycomb construction of packing. Based on the visualization of the honeycomb constructions a second heuristic judgment is obtained, according to which inside the hexagon of poles there are fragments of three GOs. The consequence is a third heuristic judgment on the plane covering density with regular packings of congruent GOs. With the help of cognitive visualization it is established that inside the hexagon of poles there are fragments of exactly three objects. The fourth heuristic judgment is related to the proposal of a triple lattice packing for regular packing of congruent GOs.