## Sunday, June 6, 2021

# Polyhedral Pendant Sculptures

It's taken me years to finish and document these hanging sculptures I started during the pandemic but here they are! Photographing these is complicated by the fact that my space is cluttered with beams, pipes, fans, and conduit, and the assemblies are big enough I would have to take them apart to get them out the door.

The first sculpture I made was this icosahedral form using circular metal rings for each of the 20 sides. The metal rings are inexpensive hoops used for flower arrangements and have a shiny golden finish. The rings are attached to each other with aluminum crimp ferrules normally used for steel cable. Because icosahedral sides are perfect triangles, I made a jig to mark each ring so the connectors were uniformly spaced at 120° intervals around the rings.

Playing around with polyhedral geometry in FreeCad (see this blog post about it) I noticed a curious thing when nesting dodecahedra and icosahedra: the centers of the edges line up perfectly! To explore this geometry, I made a dodecahedron out of the hoops, and nested it inside an icosahedron. If the sides are circles, the connectors between them must be in the center of the "edge" of the "side". Metal rods can then run through each edge to the center because they are all collinear!

I 3D printed plastic connectors to connect the hoops at the correct dihedral angle. Each clip has a top and a bottom part with grooves to capture the metal hoops at the dihedral angle. I made two sets with the different angles for docacahedra and icosahedra, but given the play of the plastic and metal, the precise angle probably doesn't matter. Top and bottom parts are held together with flathead screws; the bottoms have hex cutouts to capture nuts. Very importantly are removable when you need to get the sculpture out the door!) Each clip has a 1/16 hole through the exact center to run the metal rods.

So here's the finished icosahedron/dodecahedron (with its sister icosahedron in the background). Metal rods join in the center into a stainless sphere. I used TIG welding rods here as they are inexpensive and pretty precise 1/16" diameter. The mild steel rods are plated with a thin layer of copper. There also exists stainless steel welding rods but I liked the look of the copper -- to avoid tarnishing this, I assembled the sculpture with gloves to avoid fingerprints.

An interesting problem was how to to mark the center sphere to drill the holes for the radial rods. I solved this by 3D printing a marking jig, seen here on the right. It is one half of an icosahedron, with a round interior void the diameter of the sphere. Small holes at each edge of the icosahedron allow the sphere inside to be marked with a felt-tip pen. Since the pattern has several degrees of symmetry, the sphere can be rotated, matching up the marks with the holes, until the entire sphere is marked. Once the positions were marked, it was easy to drill them with a 1/16" bit to accept the rods.

The 3D printed icosahedron on the left has scrap welding rod ends inserted into the edges at the radial angle. This gave me the idea for the last hanging sculpture in the trio. I printed a larger version of the icosahedron, in two halves, with holes at the edges for longer rods. I then 3D printed ovoid bobbles for the ends of each rod (there are 30 of them). I then assembled it all into its midcentury Sputnik glory.

In the unlikely event anyone would ever want them, I put the FreeCAD files and STL models up on Github here: https://github.com/headrotor/freecad-polyclips.