by Dr. Chris Hill
Zometool is a mathematically-precise plastic construction set for building a myriad of geometric structures, from simple polygons to Platonic solids to models of DNA molecules to “shadows” of four-dimensional figures to works of art.
This page is intended to provide a brief introduction to Zometool and a growing collection of resources. Why create such a page? First, I'm a Zometool enthusiast (a.k.a. a Zomer). I love building with it and using it as a teaching tool. Second, I collected the information and resources on this page in the course of my own investigations and thought they may be of use to others. Third, it is my hope that some of the visitors to this page will share details of their own Zometool projects, workshops, or resources with me. In that vein, comments, questions, and suggestions are welcome! Contact Dr. Chris Hill.
Zometool has two types of parts: round connector balls and color-coded struts. The connector balls are called nodes. The unique design of the nodes allows for construction in 62 different directions. Each node has 30 rectangular holes, 20 triangular holes, and 12 pentaganal holes. The colors of the struts indicate into which holes in the nodes they will fit. Blue struts fit into the rectangular holes, yellow struts fit into the triangular holes, and the red struts and green struts both fit into the pentagonal holes. However, a green strut features two bends which cause it to point in different directions than a red strut.
Different types of struts are required for the construction of different types of structures. For example, a regular dodecahedron can be built with blue struts, a rhombic dodecahedron with yellow struts, a rhombic triacontahedron with red struts, a regular tetrahedron with green struts, and more elaborate structures with combinations of strut types.
Originally, each type of strut came in short, medium, and long sizes. In 2007, Zometool began offering super-short struts in each color. Subsequently, the company added hyper-short red struts to its repertoire of parts. For each color, the ratio between the lengths of one size of strut and the next smaller size (if there is one) is the golden ratio. (For computing such ratios, the “length of a strut” is equal to the distance between the middle of the node at one end of the strut to the middle of the node at the other end.) An elegant consequence of this fact is that in each color, the length of a long strut equals the length of a medium strut connected to a short strut. In brief, a long equals a medium plus a short. Similarly, a medium equals a short plus a super-short and, in red, a short equals a super-short plus a hyper-short.
Since the ratio between the lengths of one size of strut and the next smaller size is the same for all types of struts, a Zometool model can be scaled up (respectively, down) by replacing each strut with the next larger size (respectively, smaller size), provided that size strut exists. The company introduced super-short and hyper-short struts precisely so that users could build larger models (such as the hyperdodecahedron) on a smaller, more manageable scale.
When Zometool introduced super-short struts, it began phasing out long struts. As of 2011, long struts are no longer available from the company. However, as mentioned above, in each color, a long strut can be “built” from a medium strut and a short strut.
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