Cardboard Conglobulation

George Hart

Here's a seven-foot tall cardboard star I made with the math club at Southern Connecticut State University.  It took us about three hours to cut out and assemble the sixty pieces.  It is an intricate example of icosahedral symmetry based on a stellation of the icosahedron.

The template has six slots that are used to make all the connections. I made a cardboard master that is 38 inches long and just under 16 inches tall, so we could cut three copies out from each sheet of 48x40x0.25 cardboard.  To make your own copy, start with this pdf file.

The first step was to trace the master on sheets of cardboard with a marker. Be careful not to flip it over.  It is chiral and you need to make the parts all with the same handedness.

To cut the parts, we stacked five sheets of 16x40 inch cardboard and held them together with large binder clips. The top sheet has the template traced on it and the four underneath are blank. We used a scroll saw to cut the five sheets at once, moving the clips around as necessary.  A spiral blade went very easily through the cardboard, but cutting was the most time consuming step in the process. 

Three parts combine into a cyclic module with a three-way locking joint.

Then twenty modules are arranged more or less like an icosahedron. It is rather amorphous when beginning, but we quickly made a cycle of five modules that outline a pentagonal opening.

Some practice parts were useful so everyone could learn the three-way joint at the tips of the long arms.  It is a bit tricky to get together, but once assembled, it makes a nice lock so doesn't fall apart easily.

The construction strategy is to keep adding modules one at a time to the growing structure.  Whenever possible, position the next module to complete a cycle of five, as that adds extra strength.  It worked out best to first make the connections at the 2-fold axes, then make the 3-fold joints at the tips of the arms.

I brought along a seven-inch paper model that I made before the workshop to practice the assembly sequence and to verify I didn't make any major errors in designing the template.

This shot at the half-way point gives a nice view of the inside.  The cardboard we used is white on one side and brown on the other, adding some visual interest.  For a future version, it would be interesting to try building one with five colors of cardboard, following the five-color pattern for the underlying icosahedron.

The final module needs to be assembled inside the structure, as it wouldn't fit in through the openings. Then it can be connected into its neighbors like any other. 

The completed star is quite rigid and we suspended it from one point, so a three-fold axis is vertical.
Watch the Cardboard Conglobulation assembly video here.

A big thank you to everyone who participated, with a special thank you to Joseph Fields and Elizabeth Field for inviting me. Thanks also to Joe for taking these pictures and uploading lots more images here.