Kaleidocycles, Part 2

I’m going to spread these photos out over a few weeks. These things take about 1 hour each to make, largely because of the time it takes for the glue to dry. I’ve developed a kind of assembly line process, where I’ll make 2 or 3 objects at the same sitting, so that as the glue sets on the tabs of one object, I’ll use the time to fold or glue the other one. Initially, I was doing three of the geometric solids at one time, but when I got into the cycles, it was easier to just drop down to two. So, I’ll write them up as I work on them, and post the entries on Wednesdays, alternating with the “What’s playing” video links (youtube videos of obscure synthesizer albums).

These are the last of the solids – Icosahedron (bees), Dodecahedron (shells) and Cuboctahedron (fish). Again, there are problems with registration of the artwork over the cut and fold lines, so the finished papercrafts have white seams and misaligned lines. Also, as I was working with the paper, I’d be careful about making really strong creases, but as I glued the tabs together, the seams would soften and the finished objects would look rounder, more like balls. This was mainly an issue with the geometric solids having larger numbers of faces and that already look ball-like. Overall, though, it is fun making these and then looking at them.

The approach the authors used to tile the objects with Escher’s artwork is to identify points of rotation (where a specific object, like a bee or a bird) can be rotated around the beak or wingtip) and then draw straight lines through the rotation points across the full image. This will give you individual tiles, where one tile can be repeated over the entire surface of the object. This just leaves the choice of color map. Generally, Escher used 3, but sometimes 2 or 4 colors, the rule being that you can’t have two adjacent tiles of the same color. The authors followed this rule for the most part, but one or two of the Kaleidocycles required different mappings.

Looking at the above solids, the choice of tile patterns are pretty obvious.