I recently opted in to a “fold along” workshop (at 1am-3am local time) with Gerardo at neorigami.com and a number of guest demonstrators. The first model was a square “Vase” designed by Saburo Kase:

The process, starting with a “preliminary base” got me thinking about generalization of the algorithm to other regular polygons. The corner treatment is radially symmetrical (ie. you do the same thing on each corner), and has 3 “about here” judgement folds that all combine to control the final shape of the vessel …. so….

I cut an equilateral triangle, a new square and a regular hexagon, then formed “preliminary bases” from each geometry.

Next, I followed the corner algorithm on each of the 3, 4 and 6 corners respectively to see how it behaved. I now regret not also using a regular pentagon, as I think it would possibly be a “sweet spot” for the organic shaping … maybe some other time.

The final locking mechanism for the final facet needed a re-work for the hexagon because the internal “pocket” that provides the final lock was too shallow because of … geometry… but there was a simpler lock available via the turned in point that works nicely also.

An “algorithm” is a generalisable method that can be re-used and give the same result and the corner widget here is one such folding algorithm. You … may … have seen my “Sato Rose Algorithm” post from years back because you are an avid follower of my blog 😛 I like these re-usable bits of technique and can see me using this widget again.

Thanks to Gerardo for the invite and the fellow folders for their participation and nerdy enthusiasm.