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.
Introduction
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.
Art
- George W. Hart is a mathematician/artist who creates the most splendid and varied mathematical sculptures. Hart works in a wide range of media, including Zometool. His name appears several times on this page.
- World’s Largest Zometool Construction Assembled at the Bridges 2009 Conference in Banff by 150 mathematicians, artists, and some of their children, the mathematical sculpture has over 50,000 parts and is based on the "shadow" of a 6-dimensional cube.
- Zome-inspired Sculpture (pdf), by Paul Hildebrandt. Proceedings, Bridges London: Connections between Mathematics, Art, and Music, Reza Sarhangi and John Sharp (editors). (2006) 335-342.
- Zometool sculpture at Denver Art Museum
Book and Addenda
Company Website and Social Media
Mathematics
- The Mathematics of Zome (pdf), by Tom Davis. One of the remarkable aspects of Zometool is that, as you're building with it, when you want to connect two nearby nodes with a strut, very often the two nodes have holes of the same type and orientation lined up and there is a strut of the right length to connect them. In brief, things tend to work out. Davis provides the beautiful mathematics that underlies this phenomenon.
- Metazome, by Andrew Mihal, Matt Moskewicz, Yujia Jin, Will Plishker, Niraj Shah, Scott Vorthmann, and Scott Weber. The Metazome website proves mathematically that by using Zometool to build large meta-versions of nodes and struts, one can, in principle, construct an enormous meta-version of any Zometool model. Also see Projects, below.
- Regular Polytopes, 3rd ed., by H.S.M. Coxeter. Dover, 1973. Although written before Zometool was invented, this classic provides mathematical background for Zometool-constructible regular polytopes.
- Zome Primer, by Steve Baer. Zomeworks Corporation, 1970.
Projects
- Advanced contructions An online addendum, by George Hart, for the book Zome Geometry (see above).
- Compound of Ten Triangular Prisms This may be the most challenging of Hart's advanced constructions. It's certainly the most challenging (and satisfying) Zometool model I've ever made. The link goes to a page in Hart's website where he outlines its construction. Andrew Mihal provides an extremely helpful step-by-step procedure for building the compound, which I used to build it. Note that this model requires long yellow struts.
- Metazome, by Andrew Mihal, Matt Moskewicz, Yujia Jin, Will Plishker, Niraj Shah, Scott Vorthmann, and Scott Weber. The Zometool node has the shape of a certain polyhedron (an elongated rhombicosidodecahedron) and this polyhedron can be built using Zometool. Think of the resulting Zometool model as a significantly scaled-up node—a meta-node. Scaled-up versions of Zometool struts can also be built using Zometool, giving us meta-struts. The Metazome website shows how meta-nodes and meta-struts can, in principle, be used to construct an enormous meta-version of any Zometool model. Note that meta-struts use long struts.
- Zometool polyhedra, by George Hart. A list of some of the types of polyhedra that can be built using Zometool. These polyhedra are discussed in Hart and Picciotto's book Zome Geometry (see Book and Addenda, above).
- Zome Projects, by David A. Richter. A list of advanced projects, with varying amounts of detail for their constructions. Most of the projects are three-dimensional projections of four-dimensional figures.
Software
- vZome, by Scott Vorthmann. A program for building virtual Zome models. A version without the ability to save files is available immediately, and a fully capable version is available upon request, both at no cost.
- Zomepad Reader A program that allows the user to follow interactive step-by-step instructions for building certain Zometool models. Available at no cost from the Zometool Corporation. Using Zomepad, the user can, among other things, rotate and translate the model image, which is enormously helpful for understanding the construction. Unfortunately, as of January 2012, only a smattering of Zometool models have Zomepad files: four Tutorial Models, seven Contributed Models, and three Models-of-the-Month.
Workshops and Barn Raisings