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Zometool Workshop & Geometry Barn Raising — Fall 2011

Becca in the mega-icosahedronWondering 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).

Challenges: Round I

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 builds a truncated icosahedron while Andy constructs an elevated icosahedronNicole 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.

Brandon, Evelyn Sabina, and Colleen 

 

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.

Chris and Brandon

 

 

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.

Andy and Matt connect their elevated icosahedra

Pete and the 'Tower of Marciano'

Discussing the Round I challenges
The first round of challenges culminated with a discussion in which each participant
presented their project to the group.

Challenges: Round II

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.

Building the meta-connectors
From left to right, Andy, Becca, Colleen, Pete, and Nicole build a meta-connector.

The Barn-Raising

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.

The barn-raising begins

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!

The structure takes shape

A group effort

Some hold the structure in place so that others can add meta-connectors and meta-struts

 

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...

Repairing disconnected struts

 

 

...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.

Triumph! The students and their mega-icosahedron
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.

Becca in the mega-icosahedron

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

For more about mathematics outreach at St. Bonaventure, please contact Dr. Chris Hill at chill@sbu.edu or (716) 375-2025. To learn more about Zometool, see Dr. Hill's page of Zometool Resources.

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