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The rhombuses have simply had their centers cut out, right? You're not joining hollow segments to form the tiles, right? I tried to imagine if the "hollow segments" were triangular in cross section or only "L" in cross section, and I think I see now they're "L"s with each leg of the L an edge of a given tile.
As for the method, do you make many tiles, then connect them together (duh, of course you do) but I mean when do you remove the centers? When they're separate tiles on your work surface or when you've assembled the happymonkeygagon?
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