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

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

, a spidron is a continuous flat geometric figure composed entirely of

triangle A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC. In Euclidean geometry, any three points, when non- colli ...

s, 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.

Origin and development

It was first modelled in 1979 by Dániel Erdély, as a homework presented to

Ernő Rubik Ernő Rubik (; born 13 July 1944) commonly known by his nickname, "Little Man", is a Hungarian inventor, architect and professor of architecture. He is best known for the invention of mechanical puzzles including the Rubik's Cube (1974), Rubik ...

, for Rubik's design class, at the Hungarian University of Arts and Design (now:

Moholy-Nagy University of Art and Design The Moholy-Nagy University of Art and Design (in Hungarian: Moholy-Nagy Művészeti Egyetem, MOME), former Hungarian University of Arts and Design, is located in Budapest, Hungary. Named after László Moholy-Nagy, the university offers programs ...

). Erdély also gave the name "Spidron" to it, when he discovered it in the early 70s. The name originates from the English names of

spider Spiders (order Araneae) are air-breathing arthropods that have eight legs, chelicerae with fangs generally able to inject venom, and spinnerets that extrude silk. They are the largest order of arachnids and rank seventh in total species d ...

and

spiral In mathematics, a spiral is a curve which emanates from a point, moving farther away as it revolves around the point. Helices Two major definitions of "spiral" in the American Heritage Dictionary are:spider web A spider web, spiderweb, spider's web, or cobweb (from the archaic word '' coppe'', meaning "spider") is a structure created by a spider out of proteinaceous spider silk extruded from its spinnerets, generally meant to catch its prey. Sp ...

. The term ends with the affix "-on" as in

polygon In geometry, a polygon () is a plane figure that is described by a finite number of straight line segments connected to form a closed '' polygonal chain'' (or ''polygonal circuit''). The bounded plane region, the bounding circuit, or the two t ...

. 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. Stenzhorn reasoned that after all the initial hexagon-spidron is just the special case of a general spidron. 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; Spidron is a registered trademark. 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. The spidron is constructed from two semi-spidrons sharing a long side, with one rotated 180 degrees to the other. If the second semi-spidron is reflected in the long side instead of rotated, the result is a "hornflake". Deformed spidrons or hornflakes can be used to construct

polyhedra In geometry, a polyhedron (plural polyhedra or polyhedrons; ) is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices. A convex polyhedron is the convex hull of finitely many points, not all on t ...

called spidrohedra or hornhedra. Some of these polyhedra are space fillers.Erdély, Daniel.(2000). "Spidron System". ''Symmetry: Culture and Science''. Vol. 11, Nos. 1-4. pp.307-316. A semi-spidron may have infinitely many triangles. Such spidronized polyhedra have infinitely many faces and are examples of apeirohedra. Spidron Stefan Stenzhorn

Practical use

Considering the use of spidrons Daniel Erdély enumerated several possible applications:

References

External links

'Spidron 3D' Google image search
*
Edanet
, ''SpaceCollective.org'' * **

*{{cite journal, url=http://www.sciencenews.org/articles/20061021/bob11.asp, date=21 Oct 2006, volume= 170, issue= 17, pages= 266, title=Swirling Seas, Crystal Balls, first=Ivars, last= Peterson, journal=Science News, access-date=2006-10-21, doi=10.2307/4017499, jstor=4017499, publisher=Society for Science &, archive-url = https://web.archive.org/web/20070228210951/http://www.sciencenews.org/articles/20061021/bob11.asp, archive-date = February 28, 2007

''GamePuzzles.com'' Geometric shapes Iterated function system fractals Triangles Spirals

Origin and development

Practical use

See also

References

External links