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Glen Whitney 2024-07-14 17:30:57 +00:00
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User-Stories.md

@ -41,4 +41,6 @@ I think it will be hopeless to assemble the aaaD without a step in which multipl
- Ok, so at this point I backed off to making the smallest construction I could think of that would have enough in it that it would simultaneously solve into a non-planar configuration that should be tightly constrained enough to produce elements that will assemble rigidly into the full solution, placing each additional copy one at a time. I hit on six rectangles, surrounding two equilateral triangle faces, with two adjacent far sides of rectangles that will form regular pentagons constrained to be at 108°. That seems to curl up properly and I think it is fully constrained and will assemble into the desired unit. I should mention, though, that the first time that I built it, it folded "incorrectly" (like bad protein folding!) in that one part was convex one way and the other part was convex the other way, so overall it was not a portion of a convex solid. The only way I could find to get out of this rut was to delete some of the line segments, sort of push around the remaining elements to be closer to what I knew the solution should look like, and then put back in and re-constrain those deleted line segments. This second time I got lucky that it snapped into the desired configuration. - Ok, so at this point I backed off to making the smallest construction I could think of that would have enough in it that it would simultaneously solve into a non-planar configuration that should be tightly constrained enough to produce elements that will assemble rigidly into the full solution, placing each additional copy one at a time. I hit on six rectangles, surrounding two equilateral triangle faces, with two adjacent far sides of rectangles that will form regular pentagons constrained to be at 108°. That seems to curl up properly and I think it is fully constrained and will assemble into the desired unit. I should mention, though, that the first time that I built it, it folded "incorrectly" (like bad protein folding!) in that one part was convex one way and the other part was convex the other way, so overall it was not a portion of a convex solid. The only way I could find to get out of this rut was to delete some of the line segments, sort of push around the remaining elements to be closer to what I knew the solution should look like, and then put back in and re-constrain those deleted line segments. This second time I got lucky that it snapped into the desired configuration.
- The next step is to extrude the boxes from the six rectangular faces of the assembly, but so far I have not found a way to get solvespace to realize that they are extrudable rectangles. I can create a new workplane from two adjacent edges and a vertex, but then if I select all of the edges and vertices and hit extrude, only that one original vertex extrudes to make a line, not the whole rectangle to make a solid. Not sure if this is due to numerical issues leading solvespace not to think that the whole rectangle really lies in the workplane, or if there's just something I don't know about bringing elements into a workplane or something. - The next step is to extrude the boxes from the six rectangular faces of the assembly, but so far I have not found a way to get solvespace to realize that they are extrudable rectangles. I can create a new workplane from two adjacent edges and a vertex, but then if I select all of the edges and vertices and hit extrude, only that one original vertex extrudes to make a line, not the whole rectangle to make a solid. Not sure if this is due to numerical issues leading solvespace not to think that the whole rectangle really lies in the workplane, or if there's just something I don't know about bringing elements into a workplane or something. I was not able to figure this out after a bunch of poking around, so I [posted on the SolveSpace forum](https://solvespace.com/forum.pl?action=viewthread&parent=5783) about it, but hadn't gotten a response last I checked.
- In the end, I solved approximately by hand in GeoGebra and found that independent of the aspect ratio, the rhombi are golden, which I think will now let me do an explicit construction of the polyhedron. So guess and check by a human worked -- some luckiness that this is such a nice example (part of why I am presenting it at PCMI!)