February 2, 2022

The Polygonal method: Jay Bonner (Part 2)

The Polygonal method: Jay Bonner (Part 2)

This post will cover two other systems proposed by J.Bonner as part of the systematic method: the 3-4-6-12 and the 5-10 systems.

The 3-4-6-12 system:

The constituent polygons of the 3-4-6-12 system are the triangle, the square, the hexagon, and the double hexagon.                                                                                    

All these polygons have the same side length. Each polygon is decorated with the motifs of the four known historical families (Fig. 1).                                                

Motifs of the same family will tesselate together in innumerable ways. Figure 2 illustrates a Median 60° Pattern formed with squares, hexagons, and dodecagons.  

On the other hand, Figure 3 illustrates an Obtuse 130° Pattern formed with squares, hexagons, and dodecagons.

Fig 1: Polygons and their associated motifs of the 3-4-6-12 System

The 5-10 system:

The constituent polygons of the 5-10 system and their corresponding patterns are shown in Figure 4. These patterns will tesselate together in innumerable ways. Figure 5 illustrates a pattern created from the tessellation of decagons, pentagons, and hexagons in the median family.

Fig 4: polygonal tiles from the 5-10 system with their associated patterns
Fig 5: 5-10 pattern created from a tessellation of decagons, pentagons, and hexagons in median family