﻿ A Giant Icosahedron

## Building A Giant Icosahedron

In 2014, Southern Connecticut State University committed to hosting the Fall meeting of the Northeastern section (NES) of the MAA. As their contribution to the meeting, the SCSU Mathematics Club took on the slightly crazy project of building a ludicrously large model of the MAA logo.

The basic structure of the icosahedron was a frame of three mutually orthogonal golden rectangles made from 2-inch diameter PVC pipe. The short sides of these golden rectangles give us six of the thirty edges. The remaining 24 edges (also PVC pipe) were connected so as to join the corners of the golden rectangles. We came up with a design for joining the struts to the golden rectangles by embedding studs in the pipe elbows which make up the corners of the golden rectangles. Then eyebolts in the ends of the struts could be engaged with those studs. This design also allowed for a modicum of adjustability. Even though we were very careful in computing the sizes of our components, that adjustability came in very handy in the final stages of assembly. One major takeaway for students was confronting the "messiness" of a real-world construction versus the precision of mathematical calculation.

On the morning of the first day of the NESMAA meeting we assembled the icosahedron's frame for the first time. To everyone's joy, there were no surprises! Finally, each of the triangular regions in the surface of the frame were filled with equilateral triangles made of blue plastic tarp. We used "plastic welding" to enclose a cord in the perimeter of the tarps and then pressed grommets all around that perimeter. The manufacturing of those 20 tarps had taken up several Math club meetings and midnight oil was burned the night before the meeting by a cadre of very dedicated people.

This project involved a tremendous amount of "active learning." Students learned about geometry, trigonometry, some combinatorics and even some abstract algebra (the symmetry group of an icosahedron is isomorphic to A5 as can be seen in this virtual model.)

A gallery of images from the construction process.