Cube roots and tangents
Tinkering with an existing design, (the HOALOT cube discovered a couple of years ago), I found that only two of the six units from the original would themselves fit together to make a new cube construction. The original unit was clearly unnecessarily complex for the new cube, and I saw that the same result could be achieved from two 4×1 rectangles, or one quarter of a square. The cube holds together by friction alone: no tab fits into any pocket. Tant paper, having a slight “tooth”, works very well.
I find this Chain Link Cube curiously fascinating: it’s ridiculously simple, and yet surprisingly firm. I experimented with a variation from two 2×1 rectangles (a square cut in half) with the long sides book-folded to the centre to obtain the required 4×1 rectangle. The raw edges at the centre of the unit now provide extra friction for the other unit when the two are fitted together.
More explorations resulted in a sort of column made from six units, and a “building system” to make blocky architectural forms: this needs extra slightly modified units to make connectors.
Later I obtained a couple of identical looking cubes from single strips, each 4×1.
I don’t think diagrams for the basic cube are necessary because the principle is so simple. So I hope you can figure it out from the photos: see what else you can achieve.
Good luck, and let me know how you get on!