Robinson triangles*, introduced by R. M. Robinson are another way to build a Penrose aperiodic tiling. https://tilings.math.uni-bielefeld.de/substitution/robinson-triangle/ 

They have the advantage of representing halves of kites and darts during deflation, and can also be grouped into rhomb tilings.

These pieces are shaped in 3 dimensions to force the correct placement when snapped together. Each kite or dart is composed of two triangles, one flipped relative to the other, and connected at the rectangle jigsaw tab.

*Note that Robinson's deflation rule (shown in the link) uses a larger obtuse triangle and a smaller acute triangle, in keeping with how these split into rhombs. I have included a photo of how all these shapes decompose into the pieces here.

If you want your tiling to look like rhombs rather than kites and darts, there are two ways. 

You can use these alternative Robinson tiles which represent thick rhomb halves directly.

Another approach is just to print some kite halves in the same color as dart halves and compose thick rhombs as shown below.