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I have been interested in overlapping tiling recently. Ive made a few cool designs, but I cant think of any use for overlapping tiles in 2 dimensions. Using overlapping tiles to create a sphere has a purpose, because the fact that the tiles are overlapping holds the sphere together.
in the link shows my overlapping shell sphere design. This tiling has 8 sphere segments (shells) of the same size and shape (the blue and purple elements), and 6 curved cross shaped elements (grey). The cross shaped elements are created flat from a resilient material, and bent to fit into the gaps between the blue and purple shells.
How/why it works:
The two inside edges of the resilient crosses push against the purple shells outward, but the purple shells are kept in place by the blue shells. The purple shells push against the blue shells, but the blue shells are kept in place by the outside edges of the resilient crosses.
Constructing this would be tricky since it would only be stable once all the shells and resilient crosses are in place. It could be done with scaffolding, wherein all the shells are held in place, then the resilient crosses are inserted.
This could be used as an interesting spherical packaging for toys. Once a single resilient cross is removed, the whole sphere falls to pieces.
This design is based on a truncated octahedron. Interestingly only two other designs could be made (based on the great rhombicuboctahedron or the great rhombicosidodecahedron), using the same kind of overlapping design.
resilient shell sphere
[xaviergisz, Feb 06 2006, last modified Dec 13 2011]
including the truncated octahedron, the great rhombicuboctahedron and the great rhombicosidodecahedron [xaviergisz, Feb 06 2006]
why didn't I think of this?! [xaviergisz, Apr 06 2013]
Something similar, but it inverts.
[2 fries shy of a happy meal, Apr 09 2013]
||[21 Quest], I think this is a little different to the ball in your link.
||from the link: //We use the ball puzzle as a foraging toy. One piece slides in and out like a drawer. We put a treat inside.// which is quite different from how mine works. The pieces in mine do not slide in and out like a draw. The 8 shell pieces are carefully arranged, then the resilient crosses are bent (perhaps flexed is a better word) to fit in the gaps.
||That design in the first link is brilliant!
||How does an idea this good drop like a stone? (+)
||Hear, hear! It's one of those things I couldn't even
think of thinking of myself. Very elegant.
||Used to buy lots of something that looks like a more complicated version of this idea in the 100Y shop in Japan, the kids enjoyed playing with them.
||From a functional point of view, they are very energy absorbent and would make neat crash bags for landing stuff on Mars.
||Flat-pack soccer balls, love it.[+]