Wondering what exactly is happening in the curious photo to the left? It all began with St. Bonaventure's first Zometool Workshop, organized by Dr. Chris Hill, Assistant Professor of Mathematics, and Evelyn Sabina, Curator of Education at The Regina A. Quick Center for the Arts.
The purpose of the two-hour workshop, held November 9, 2011, was to allow high school students to explore geometry using a construction kit called Zometool. The workshop culminated with a "geometric barn-raising": students and teachers worked together to build a very large structure called a mega-icosahedron.
Sabina recruited mathematics teachers Todd Christopher of Allegany-Limestone High School and Kris Ring of Olean High to invite talented math students from their schools. The student participants were Colleen Bailey, Brandon Kohn, Chris Spears and Pete Marciano II from Allegany-Limestone and Andy Lu, Matt Witte, Becca Lasky and Nicole Sova from Olean High. The students were joined by Allegany-Limestone teachers Linda Dodd-Nagel and Tammy Hollowell and Bonaventure MSED student Jackie Donovan, in addition to Todd Christopher and Kris Ring.
Sabina also provided the perfect venue: a large student-oriented space on the third floor of The Quick Center called The Loft. Read further for the story of the workshop (and of the photo).
To familiarize the participants with Zometool, they were given challenge sheets with projects such as the-cube-in-the-dodecahedron, the elevated icosahedron, and the rhombic triacontahedron. However, participants were free to modify the projects or work on their own projects.
Nicole discovered the "scaffolding" method for building certain polyhedra. She put medium blue struts in all rectangular holes in a connector ball to create a blue "pin cushion". By putting connector balls on the ends of the blue struts and then connecting those balls with more blue struts, Nicole created a truncated icosahedron.
Andy built an icosahedron, on the way to an "elevated" icosahedron, which is a kind of three-dimensional star. The completed model appears in some of the photos below.
In the photo to the right, Brandon discusses one of his projects with Evelyn Sabina. Prior to the Round I challenges, Brandon built a model that, remarkably, included two of the challenges: a regular dodecahedron and a rhombic triacontahedron.
To the right, Colleen constructs a regular dodecahedron on the way to the cube-in-the-dodecahedron. An avid equestrienne, Colleen also built a horse, which stands alertly in the middle of the table.
During the first round of challenges, Chris (to the left) and Brandon built different varieties of dodecahedra: Chris built a regular dodecahedron and Brandon assembled a rhombic dodecahedron.
At right: Pete tests the local supply of medium blues and the room’s vertical clearance with the “Tower of Marciano”. The tower is topped by a blue dodecahedron and a red triacontahedron.
Below: Andy and Matt connect their elevated icosahedra.
The first round of challenges culminated with a discussion in which each participant presented their project to the group.
In preparation for the barn-raising, each participant was challenged to build a "meta-connector", that is, a beachball-sized model of the Zometool connector ball. A connector ball has the shape of a polyhedron called an extended rhombicosidodecahedron, and this polyhedron can be built with Zometool. We needed twelve meta-connectors for the barn-raising, so with thirteen participants, we had enough plus one as a backup.
From left to right, Andy, Becca, Colleen, Pete, and Nicole build a meta-connector.
With the meta-connectors complete, the students began connecting them with "meta-struts" to build a mega-icosahedron. The mega-structure would have the shape of a regular icosahedron, which is a three-dimensional figure with 20 faces (sides), each an equilateral triangle.
Above: the triangular base has been built. Just 19 more triangular faces to go! Notice the small icosahedron at the lower right corner of the photo. The students used the small model to guide the construction of its much larger cousin.
To the right: as meta-connectors are attached to the base
with meta-struts, the structure begins to take shape.
Below: it takes a lot of people to raise a barn!
As the mega-icosahedron neared completion, it became free-standing. Until then, the "sides" had to be held to prevent the structure from collapsing while more meta-connectors and meta-struts were added.
Meanwhile, near the bottom of the structure...
...the stresses caused by the vigorous activity above repeatedly disconnected some of the struts.
But soon the structure was complete and all broken connections repaired.
Congratulations—it's a mega-icosahedron! From left: Becca Lasky (front), Matt Witte,
Chris Spears, Nicole Sova, Andy Lu, Pete Marciano II, Brandon Kohn and Colleen Bailey.
The towering structure contained over 2500 parts and...
...was large enough that...
...Becca Lasky was able to gingerly enter and stand up inside of it.
For more information about educational outreach programs coordinated by The Quick Center at St. Bonaventure, visit the Center's Arts Education webpage.
Zometool is an easy-to-use yet mathematically precise plastic construction kit. It has two types of parts: round connectors and color-coded struts. The unique design of its round connectors allows for construction in 62 different directions, enabling users to build a myriad of geometric structures, from basic shapes such as triangles and rectangles to Platonic solids to models of DNA molecules to “shadows” of complex four-dimensional figures.
Zometool is an excellent educational tool. Besides being challenging and fun, model-building projects help students visualize abstract concepts, understand spatial relationships, perform mathematical investigations, and unleash their creativity. Such projects are as meaningful to math students as they are to students of engineering, architecture and art.
For additional information about Zometool workshops and projects and related resources, see our Zometool Resources page.
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