Intro: Geometric Sculpture From 72 Pencils
George W. Hart is a sculptor of constructive geometric forms (and writer of the Math Monday columns at Make), and I've long been an admirer of his work. Reproducing his art is far from trivial - I once tried to build his Chronosynclastic Infundibulum, but broke so many CDs I gave up in disgust. However, I recently discovered that Alejandro Erickson, instructable-r and self-confessed mathemagician, lives in the same city as me and runs workshops on geometric construction, so we hired him for an afternoon. He was the great geometry guru we'd hoped he'd be, and he kept 6 kids and 3 adults well entertained and busy making tensegrities. As a special request, he also taught two of us how to make a replica of Hart's 72 pencils sculpture (Hart made a limited edition of 19 unique examples of these). It took a couple of leisurely hours to build and glue, and with supervision was surprisingly easy to make. It can be assembled inexpensively using wooden pencils (conveniently sold in packs of 72!), a few rubber bands and a little superglue, in pretty much exactly the same way as Alejandro makes his Hexastix sculptures (see below for the video). The hexagonal cross-section of the pencils make them a very natural fit for this geometric form, as the holes in the lattice are themselves hexagonal. The erasers are arranged tetrahedrally with respect to one another; the volume enclosed by the pencils is a rhombic dodecahedron. It's a neat piece of art that I'm pleased to own; many thanks to George W. Hart for the inspiration and Alejandro for the instruction!
I made a variant of this sculpture using 76 pencils, in which the pencils form six-pointed stars rather than hexagons. I used colored pencils for that one, but couldn't find a nice set of exactly 76. There are good sets of 72 colored pencils available, though.
Video: Follow Alejandro's instructions, but build only as far as a hexagon consisting of a ring of 18 pencils, removing the inner pencils as you go. If you find the erasers aren't arranged tetrahedrally (as I did), just invert one ring one pencil at a time until your sculpture looks like the original. Superglue the joints before removing the rubber bands.
Step 1: Builds
Happily, lots of people have made this sculpture, and some of them have shared their builds with me. They've often been very creative too, using among other things BBQ skewers, copper pipe, pvc and toothpicks! Thanks to guerroloco, jayefuu, EVM, akarod79, palmsco, mrpesas, XP1 and innovationcreation for sharing.