Spidron

First Spidron after Dániel Erdély

A spidron is a complex geometric figure made up of a series of isosceles, equilateral triangles , two triangles each forming a hexagon , a regular hexagon that is connected to another hexagon by connecting one corner point to the next but one corner point. This allows the shape to be nested into a variety of structures. These have already been examined mathematically. The name arose from the English terms spider (spider) and spiral (spiral), as the shape of the spidron is reminiscent of a cobweb .

definition

A classic spidron in a hexagon

The starting point of the classic Spidron is a regular hexagon with the edge length a. Each corner point is connected to the next but one corner point (i.e. two corners further) by a segment. The connecting lines intersect at six points of intersection. For reasons of symmetry, a smaller, regular hexagon is created inside. This new hexagon can be subdivided in the same way as before. If one continues this generation of hexagons indefinitely, one arrives at a sequence of ever smaller triangles. The resulting figure is called Spidron. "

Origins and Development

Spidrons were discovered in 1979 by the Hungarian design student Dániel Erdély . The shapes were part of a housework by Erdély. He was encouraged to do this by Ernő Rubik , the inventor of the Rubik's Cube , during his studies at the Moholy Nagy University for Handicrafts and Design in Budapest .

Spidron relief after Stefan Stenzhorn

In his first work, Erdély assumed a regular hexagon for the construction of Spidrons. However, spidrons can be generated from all regular n-vertices whose vertex number is greater than four. In addition, the connection can be extended by two corners to connection lines by m corners. According to Stenzhorn, one therefore comes to the conclusion that a spidron in a hexagon is only a special case of a general spidron.

Furthermore, the corner points of a Spidron form a logarithmic spiral . In his first work, Erdély gave the figures he found different names. He called one half of the Spidron a “semispidron”. Depending on how two “semispidrons” were placed next to each other, Erdély defined other figure names such as “B-Spidron”, “J-Spidron” or “Hornflake”. Ultimately, however, all the assembled figures can be traced back to the term spidron used here.

Practical use

The shape is known from many of Escher's works , who preferred to devote himself to such bodies with high symmetry . It is generally known that with the help of regular hexagons a two-dimensional plane can be tiled without gaps. Since each hexagon has six Spidronarmen is also Spidrons a complete tiling of the plane possible.

Regarding a three-dimensional spidron, Stefan Stenzhorn writes : "The spidron offers the possibility of being shaped three-dimensionally so that reliefs can be created from it. The starting point are the six spidrons of a hexagon. Three spidrons are folded in such a way that each fold is a mountain fold The other three Spidrons are folded so that each fold is a valley fold. ". With regard to Spidron reliefs, Erdély sees possible areas of application e.g. B. as a shock absorber or crumple zones. He also sees an application in space travel as possible. In addition, a Spidron relief in a solar system could more easily capture the sun.