Pappenheim cell

The Pappen-Heim cell is an interesting and little-studied topic in mathematics and physics. It was discovered by German physicist Niels Hoogen in 1974. It is a grid consisting of squares that are painted according to a color scheme of four colors. Each square has two adjacent squares of the same color, alternating colors. Fix the colors vertically and horizontally when applying the design to the paper. It is a very simple structure, yet it has interesting properties related to its physical properties and is used in various fields of science.

Let's consider the properties of the Papapen-Heim cell. There are three types of squares, depending on the number of intersections within the square. In this case, they are also called invariants. Each cell can have either one, two, or three intersections within it. Let's call them A-cells, B-cells and C-cells, respectively. It is important to note that A-squares usually have two adjacent intersections of the same color. This type of squares is especially interesting. Keeping two or more identical cell colors together is easier than different colors, so Papenheim squares should retain much of their structure and remain functional for applications. There are several possible uses for the Papenheim cell if we study its complete structure.

The Papenheim cell is also seen as an example of geometric and topological features