Zometool
Zometool is a construction set toy that had been created by a collaboration of Steve Baer (the creator of Zome architecture), artist Clark Richert, Paul Hildebrandt (the present CEO of Zometool), and co-inventor Marc Pelletier.
The learning tool was designed by inventor-designer Steve Baer, his wife Holly and others.
The Zometool plastic construction set toy is produced by a privately owned company of the same name, based outside of Longmont, Colorado, and which evolved out of Baer's company ZomeWorks.
Its elements consist of small connector nodes and struts of various colors.
The ends of the struts are designed to fit in the holes of the connector nodes, allowing for syntheses of a variety of structures.
The idea of shape-coding the three types of struts was developed by Marc Pelletier and Paul Hildebrandt.
To create the "balls," or nodes, Pelletier and Hildebrandt invented a system of 62 hydraulic pins that came together to form a mold.
[3] In the years since 1992, Zometool has extended its product line, though the basic design of the connector node has not changed so all parts to date are compatible with each-other.
From 1992 until 2000, Zometool produced kits with connector nodes and blue, yellow, and red struts.
In 2000, Zometool introduced green struts, prompted by French architect Fabien Vienne, which can be used to construct the regular tetrahedron and octahedron.
The struts "with clicks" have a different surface texture and they also have longer nibs which allow for a more robust connection between connector node and strut.
[citation needed] The color of a Zometool strut is associated with its cross section and also with the shape of the hole of the connector node in which it fits.
The cross section of a green strut is a rhombus of √2 aspect ratio, but as the connector nodes do not include holes at the required positions, the green struts instead fit into any of the 12 pentagonal holes with 5 possible orientations per hole, 60 possible orientations in all; using them is not as straightforward as the other struts.
At their midpoints, each of the yellow and red struts has a twist where the cross-sectional shape reverses.
This design feature forces the connector nodes on the ends of the strut to have the same orientation.
Similarly, the cross section of the blue strut is a non-square rectangle, again ensuring that the two nodes on the ends have the same orientation.
Instead of a twist, the green struts have two bends which allow them to fit into the pentagonal holes of the connector node which are at a slight offset from the strut's axis.
[citation needed] Among other places, the word zome comes from the term zone.
Due to this length ratio, the blue-green struts that have a rhombic cross section do not mathematically belong to the zome system.
[citation needed] The strut lengths follow a mathematical pattern: For any color, there exists lengths such that they increase by a constant factor of approximately 1.618, a number that is yield of what is called the “golden ratio" which is represented by Greek letter phi (
, equipped with the standard inner product, also known as 3-dimensional Euclidean space.
There are then 30, 20, and 12 standard vectors having the colors blue, yellow, and red, respectively.
Correspondingly, the stabilizer subgroup of a blue, yellow, or red strut is isomorphic to the cyclic group of order 2, 3, or 5, respectively.
Hence, one may also describe the blue, yellow, and red struts as "rectangular", "triangular", and "pentagonal", respectively.
The zome system may be extended by adjoining green vectors.
One may then enhance the zome system by including these green struts.
The converse of this fact is only partially true, but this is due only to the laws of physics.
[citation needed] The zome system is especially useful for modeling 1-dimensional skeletons of highly symmetric objects in 3- and 4-dimensional Euclidean space.
However, many other mathematical objects may be modeled using the zome system, including:[citation needed] The uses of zome are not restricted to pure mathematics.
Other uses include the study of engineering problems, especially steel-truss structures, the study of some molecular, nanotube, and viral structures, and to make soap film surfaces.
