Spidron

This article discusses the plane geometric figure; for the science-fiction character see Spidron (character).

First spidron created by Dániel Erdély in 1979

In geometry, a spidron is a continuous flat geometric figure composed entirely of triangles, where, for every pair of joining triangles, each has a leg of the other as one of its legs, and neither has any point inside the interior of the other. A deformed spidron is a three-dimensional figure sharing the other properties of a specific spidron, as if that spidron were drawn on paper, cut out in a single piece, and folded along a number of legs.

Spidron created from a triangle.

Origin and Development

Spidron Hexagon

It was first modelled in 1979 by Dániel Erdély, as a homework presented to Ernő Rubik, for Rubik's design class, at the Hungarian University of Arts and Design (now: Moholy-Nagy University of Art and Design). Also Dániel Erdély gave the name Spidron to it, when he discovered it in the early 70s.^[1] The name originates from the English names of spider and spiral, because the shape is reminiscent of a spider web.

In his initial work Erdély started with a Hexagon. He combined every corner with the after-next one. In his mathematical analysis of Spidrons Stefan Stenzhorn demonstrated that it is possible to create a Spidron with every regular Polygon greater than four. Furthermore, you can vary the number of points to the next combination. Stefan Stenzhorn reasoned that after all the initial Hexagon-Spidron is just the special case of a general Spidron.^[2]

In a two-dimensional plane a tessellation with Hexagon-Spidrons is possible. The form is known from many works by M.C. Escher, who devoted himself to such bodies of high symmetry. Due to their symmetry Spidrons are also an interesting object for mathematicians.

The spidrons can appear in a very large number of versions, and the different formations make possible the development of a great variety of plane, spatial and mobile applications. These developments are suitable to perform aesthetic and practical functions that are defined in advance by the consciously selected arrangements of all the possible characteristics of symmetry. The spidron system is under the protection of several know-how and industrial pattern patents. It was awarded a gold medal at the exhibition Genius Europe in 2005. It has been presented in a number of art magazines, conferences and international exhibitions. During the last two years it has also appeared, in several versions, as a public area work. Since Spidron-system is the personal work by Dániel Erdély but in the development of the individual formations he worked together with several Hungarian, Dutch, Canadian and American colleagues, the exhibition is a collective product in a sense, several works and developments are a result of an international team-work.

Spidron is a registered trademark

Many spidrons are designed to correspond to deformed spidrons that are also polyhedra.

Spidron Relief created by Stefan Stenzhorn

Practical Use

Considering the use of Spidrons Daniel Erdély enumerated several possible applications: "It has been raised repeatedly that several layers of spidron reliefs could be used as shock dampers or crumple zones in vehicles. Its space-filling properties make it suitable for the construction of building blocks or toys. The surface could be used to create an adjustable acoustic wall or a system of solar cells that follow the sun in a simple manner. Various folding buildings and static structures could also be developed on the basis of my geometric investigation which may have utility in space travel." ^[3]

References

External links

• Spidron Main page
• Spidron Geometric Systems
• New Developments
• The Pécs Exhibition on Spidron homepage
• Peterson, Ivars (21 Oct 2006). "Swirling Seas, Crystal Balls". Science News. Society for Science &#38. 170 (17): 266. doi:10.2307/4017499. JSTOR 4017499. Archived from the original on February 28, 2007. Retrieved 2006-10-21. 
• Stefan Stenzhorn Spidrons Spidrons and mathematics