art and science at play art and science at play ® Tip: Zometool is particularly suitable for 3 ® symmetric tessallations. Sir Roger Penrose ZOMETOOL employed Zometool whilst working on his ZOMETOOL design series “Penrose Tiling”. As is the case with all exceptional developments, Zometool is the left: Paul Hildebrandt, above: „Cubespace avec Zometool“ by Fabien Vienne, The symmetrical beauty of Zometool models is enhanced and hypercube. We call this model “Speedy Hypercube” and result of many inspirational events and occurrences. right: Zometool construction in Coimbra Portugal, “Bridges Conference 2011”. accentuated by the black and white struts and balls of the you can see a smaller version of the same model on the Design Series. You can create a great variety of models and 1 base of the Design 3 box. In the mid 1960’s, “Drop City”, a living environment conceived and During the 1980’s, inspired by Steve Baer’s work, Paul Hildebrandt structures with Design 3. 3a created by art students and film makers in southern Colorado, and Marc Pelletier began working together to revitalise and enhance Model 3. In order to construct a hypercube with centralised Zometool. 10 years of exacting work were required, but the result Speaking of symmetry, let’s take a closer look at the cube. The perspective, build a cube using medium (B2) struts and place was an ingenious design for a connecting ball, which, in combination symmetries of the cube are defined by the uniformity of its edges, another cube, made of super-short (B0) struts in the centre. with struts in specific shapes and colours, makes it easy for children vertices and surfaces. The cube, also referred to as a regular Connect the corners of the two cubes with 8 short (Y1) and adults alike to build and play with Zometool. The very first hexahedron (greek: Hexaedron) is one of the five Platonic Solids triangular struts. Of the 8 cubes, 6 appear as truncated Zometool ball was produced in April 1992 - and it was perfect. (see the Zometool kit Plato’s Solids), or, to be more precise, a pyramids (3a). Illustration 4 is a depiction of the shadow polyhedron (a form with multiple surfaces). projection of your model. Drop City Panorama, Colorado, USA The struts are produced in three different shapes, which fit into 2 4 the respective openings of the ball, and in three lengths, which Model 1. With Design 3 you can build a cube, using 12 medium These cube variations are only a few examples of the came into being. Inspired by Buckminster Fuller’s architectural conform to the rules of the “Divine Proportion” (Golden Ratio). (B2) struts, in either black or white - or you can mix the models which you can create with Zometool: the ideas, the “Droppers” designed their living quarters and studios on The strut forms, together with the precise arrangement of the colours; just as you like. The rectangular opening should possibilities are almost infinite. The illustrations on the basis of geometric solids, for example, triacontahedrons and openings, enable not only the portrayal of complex mathematical always be uppermost in this case. If you have built a white the base of this box offer a few further ideas of what other “zonohedrons”. In 1967, Buckminster Fuller awarded Drop structures: Zometool links imaginative play with art, science and cube, build a cube of the same size in black. Take 8 super- you can build with Design 3. The black and white City the Dymaxion Prize for innovative und economical architecture. research. Complying with the rules of natural geometry, Zometool short triangular struts (Y0) and connect the two cubes at balls and struts of the Design Serie allow you to Steve Baer, an architect who often visited Drop City, developed a models are always well proportioned, harmonious structures - the corners (model 2). A parallel projection of a cube will accentuate the various surfaces, vertices and edges toy for children on the basis of these constructions: Zome Toy. an inspirational medium for artistic expression. emerge. You have taken the first step towards builing a of your models. art and science at play ® To see a world in a grain of sand art and science at play art and science at play ZOMETOOL And a heaven in a wild flower, ® ® Hold infinity in the palm of your hand glossary and eternity in an hour. William Blake Buckminster Fuller: *12.7.1895. ¦ 1.7.1983 in USA; architect, visionary, philosopher ZOMETOOL ZOMETOOL and author. Particularly renowned for his “domes” and geodesic architecture. Dimension: informally defined as the minimum number of coordinates needed to Zometool Rules The components of the Zometool Design Series are naturally compatible specify any point within a space or an object. Drop City: artists’ community, founded in 1965 by Gene Bernofsky, JoAnn 1. If it works, it works perfectly… with all other Zometool kits. Bernofsky, Clark Richert and Richard Kallweit in Colorado. …and if it doesn’t work, it doesn’t work at all. Dymaxion: a definition created by Buckminster Fuller; abbr. of dynamic maximum Don’t force Zometool components. You can bend a strut to fit it into a tight spot, Hypercube tension. Used as a trade name for Fuller’s developments (cars, houses, etc). but struts in finished models are always straight, never under tension. Hypercube: cube in the 4th. dimension. Tessellation: also known as tiling, mosaic; a method of filling a space with identical 2. Don’t break it apart, take it apart! forms, without overlapping. Take models apart by grasping a strut with your fingers and pushing the ball Penrose, Sir Roger: *8.8.1932 in Essex, England. Mathematician and theoretical straight off with your thumb. Twisting balls or pulling models apart or crushing physicist. Discovered and developed “Penrose Tiling”, forms with 5-fold symmetry, them can cause parts to break! which fill a space (see “Tessellation”). Projection: image of an object (also called “shadow”) on a 2-D surface, whereby Thanks to: the points of a 3-D object are shown in 2-D. Photo “Drop City Panorama”, Clark Richert, USA; (Drop City was founded in Rhombic icosidodecahedron: Polyhedron (multi-sided), born of the family of 1965 by Gene Bernofsky, JoAnn Bernofsky, Clark Richert & Richard Kallweit.); archimedean solids. Consists of 20 regular triangles, 30 squares and 12 “Cubespace” drawings (1999) with kind permission of Fabien Vienne; Photo regular pentagons. P. Hildebrandt: Erwin Kotzab 2011; Photo of the construction in Coimbra: Jim “Kepler’s Kosmos” and “Creator 1”: just a small taste of the many possibilities in Rhombus: every parallelogram with equal side lengths. Hausman. Software for model images: Dr. Scott Vorthman; Text and design: the extensive and versatile Zometool Universum. Symmetry: the effect achieved when forms are mirrored on a point, an axis or a plane. Erwin Kotzab and Lyn Taylor. design Zometool Europa UG · Rainbühlgasse 7 · D 87541 Bad Hindelang Tel.: +49 (0)8324-9336040 · Mail: [email protected] © 2012 Zometool Europa UG. Based on the 31-zone system, discovered by Steve Baer, Zomeworks Corp., USA © 2011 Internet: www.zometool.com