76 Pencil Sculpture

A few years back I was taught how to make a replica of George Hart's 72 pencils sculpture:

Here, I've remixed this idea to make a variant sculpture. It now uses 76 pencils, but this time they're arranged as four interpenetrating six-pointed stars rather than hexagons. It cost about $11 and took about an hour to construct. It's easier to make than the original, because there is no need to replace the pencils as you go - they are all placed in their final positions. The 28 and 52 pencil versions of the sculpture are also quite nice, if you don't have enough pencils for the 76 handy.

Step 1: Materials

You need 76 pencils and at least 60 tiny rubber bands. If you want to make your sculpture permanent, you will need some superglue. I used a pack of mixed coloured pencils (~$10) and a Rainbow Loom a few Rainbow Loom-style rubber bands (a few cents). I decided to divide the pencils semi-randomly - each of the four directions would be reds/pinks, yellows/oranges/browns, greens, and blues/purples. You need 19 pencils for each direction (one central one, and three rings of six).

Step 2: Initial Assembly

I've included Alejandro's video below because it really nicely shows you how to do the first few steps of the build, which are the tricky ones. These are made up of groups of pencils pointing in four different directions (tetrahedrally arranged, for those interested in geometry, which means each pencil is either parallel to or at 109.5° to the other pencils in the structure). I chose to aim all the points upwards, so the sculpture has a maximally spiky exterior, but arrange how you see fit.

Start by making a group of 7 pencils. Put a rubber band around them. Take two pencils, and split these into 2:3:2, and do the same with another two pencils in a different direction. Repeat to make two layers of two pencils in each direction. Put rubber bands around all ends. Now place the pencils on the table in a three-legged stool, and look straight down, trying to find an arrangement where you can see four hexagonal-shaped holes. Put pencils through these, and rubber band each end.

Step 3: 28 Pencils

Complete 7 pencils in a ring around the central one for all four directions. Replace the encircling rubber band with three securing three pencils in a row at each end. This helps keep the central pencil in place. This trick isn't shown consistently in the photos, because I didn't figure it out until later in the build.

Step 4: 52 Pencils

Now add another pencil in positions radiating out from the center, securing each one as you go with a rubber band that goes around three pencils in a row. You won't be able to do all six in each direction until you have added extra ones in other directions; just work your way around slowly. You've done all the hard stuff already.

I actually quite like the 52 pencil sculpture. You may just want to stop at this point rather than add the final ring.

Step 5: 76 Pencils

Repeat the previous step, adding a new rubber band for each pencil. And you're done!

You can make your sculpture permanent by supergluing the joints and removing the rubber bands. The sculpture may look like it should hold together by itself, but it won't. Don't take my word for it, though - you should try it yourself...