Spidron

A Spidron is a complex geometrical figure of a series of isosceles, equilateral triangles, two triangles are each a hexagon, form a regular hexagon, which is connected to a further hexagon, by using a vertex on the next vertex is connected. In this way the shape can be interleaved in a variety of structures. These have also been studied mathematically. The name originated from the English names spider (spider) and spiral ( spiral), because the shape of Spidrons reminiscent of a spider's web.

Definition

Starting point of the classic Spidrons is a regular hexagon with edge length a Each vertex is the vertex of the next (ie two blocks away ) by a distance. The links intersect at six intersections. For reasons of symmetry is created inside a smaller, regular hexagon. This new hexagon can be divided in the same manner as before. Substituting this generation of hexagons infinite continues, so we arrive at a sequence of smaller and smaller triangles. The resulting figure is called Spidron. "

Origins and Development

Were discovered in 1979 by the Hungarian Spidrons design students Dániel Erdély. The forms were part of a research project from Erdély. He was animated to during his studies at the Moholy - Nagy University of Art Craft and Design in Budapest from Ernő Rubik, the inventor of the Rubik's Cube.

In his first works Erdély went out in the construction of Spidrons still of a regular hexagon ( hexagon ). Spidrons you can generate whose Eckzahl is greater than four, however, from all the regular n - corners. Moreover, the connection will be extended by two corners connecting lines to m vertices. After Stenzhorn one comes to the realization that a Spidron in Hexagon just a special case of a general Spidrons is.

The principle that the vertices of a Spidrons form a logarithmic spiral. In his first works were found Erdély the characters different names. A Spidron - half he described as " Semispidron ". Depending on how two " Semispidrons " were placed together Erdély defined more character names, such as " B- Spidron ", " J- Spidron " or " horn Flake". Ultimately, however, can all be composite figures on the Spidronbegriff used here lead back.

Practical Application

It is known to form out of many works of Escher, which is preferably such bodies devoted himself with high symmetry. It is generally known that with the help of regular hexagons a two-dimensional plane can parqueting gaps. Since each hexagon consists of six Spidronarmen, even with Spidrons a complete tiling of the plane is possible.

In terms of a three-dimensional Spidron Stefan Stenzhorn writes: "The Spidron offers the opportunity to become three-dimensional shape, so that it is possible reliefs produced from that starting point are the six Spidrons of a hexagon are three Spidrons folded so that each fold a Bergfalz. . is. Spidrons The other three are folded so that each fold is a Talfalz. ". With regard to Spidron - reliefs looks Erdély possible application areas such as as a shock damper or crumple zones. Also an application in space he sees as possible. In addition, could easily capture the sun in a solar system Spidron - reflief.