I really love the idea of combining 3D printed elements with traditional materials, to go beyond what's achievable with either in isolation. And, in that spirit, I designed this vase, which is constructed of printed tiles that are to be laced or sewn together. The triangle tiles are rounded and have a channel around the outside to let them support each other when assembled.
LET'S TALK GEOMETRY!
The base of the vase is a hexagon, and from there we have layer after layer of triangles. First a row pointing up, then a row pointing down, and so on. But, the key thing is that these are isosceles triangles, and while the third size and the overall height might vary between tiles, the two sides that match are always the same on every tile. So, say you have some medium-sized triangles that are pointing up, and you're ready to add a layer of triangles pointing down. If you use narrower triangles, the vase will get narrower. likewise, if you use broader triangles, it will flare out. So, by varying the triangles on each layer, the shape of the vase comes to be. As long as the triangles have that consistent length on the two equal sides, everything will work out.
Included here are three triangles, named 20, 50, and 80. That's actually just the nominal width of the base, smoothing and such notwithstanding. The medium triangle is equilateral, so all sides are 50. The base is just a regular hexagon (neatly smoothed) that has a 50mm side.
If you want to reproduce the vase in the photos, the layers are: base, 50, 80, 80, 80, 50, 50, 20, 20, 50.
Oh, and one more thing - as is probably obvious, each layer that points up needs to be the same size as the one below it that points down.
If you want to make your own tiles of different sizes, the easiest thing to do is just to resize the equliateral tile. The holes will end up non-round, of course, but that's nothing to stress over. You'll need to know how tall a tile needs to be for a given base, though, and for that, Pythagoras is your friend.
height = sqrt(1 - ((base/50)^2)/4)) * 50
Well, no, this isn't going to hold water very well. But, I'm not sure I trust any printed object to hold water, unless it's been epoxied inside, which you technically could do with this, if you used enough epoxy...
Anyway, have fun!