One of my favorite polyforms are polysticks on a hexagonal grid. These critters consist of connected collections of grid edges.
I stipulate that whenever two edges of a polystick meet, we add a a joint to the figure. This is in order to avoid indecent intermingling of legs as shown by the two polysticks in the figure below. Blush. The properly decorated green polystick can only watch in dismay.
We want to use the polysticks as puzzle pieces, and we want to keep things simple. So here are all four hexagonal polysticks with three legs and just one joint. I like to call them triffids.
Two of them are symmetric by reflection, so I leave it up to you to count them as one or two. We can us three of them to tile a small triangle easily like so:
By tiling I mean that we want to cover all the edges of the given shape, do not allow that two polysticks share a leg or joint (what a thought!), and do not require all vertices to be covered. We could do so, limiting the possibilities dramatically.
Below are two more examples. First a larger triangle, tiled using three kinds of triffids.
I have not found a way to tile this triangle (or a larger one) with just one kind of triffid. And here is a hexagon that uese all four triffids to be tiled:
Now go and make your own. If you want to use triffids, make sure that the number of edges of your shape is divisible by 3.
The Inner Frame 