*** UPDATE 2020-08-11 ***
I've added a third variant which is a non-polypanel version that can be used like a regular jigsaw puzzle (see update info following the original description). The models in this download are now as follows:
Version 1 - Original polypanel design (two rhombuses)
Version 2 - Improved polypanel design (two rhombuses) -- NEW 2019-05-20
Version 3 - Non-polypanel jigsaw puzzle version (two rhombuses in both STL and Fusion 360 formats) -- NEW 2020-08-11
These two polypanels can be used to create a Penrose tiling pattern that never repeats no matter how many tiles you use.
For this to work, you have to match up the features on the faces of the two different rhombuses like a jigsaw puzzle. Both of the rhombuses have a segment of a curve and a segment of a filled circle on their faces that have to be matched with adjacent tiles.
When the tiles are combined according to this rule, some pleasant semi-regular patterns emerge, but the pattern as a whole never ever repeats!
This clever tiling pattern was discovered by the mathematical physicist Roger Penrose. For more information about it, have a look at the Penrose tiling page on Wikipedia.
The two rhombuses in this upload have standard polypanel side lengths but differ from the polypanel rhombus that Devin Montes created by having different internal angles. In this case, they are 72 and 108 degrees for the wider rhombus and 36 and 144 degrees for the thinner one, whereas Devin's rhombus has internal angles of 60 and 120 degrees.
Notice that 72 degrees divides a circle 5 times and 36 degrees divides it 10 times so there ends up being a lot of five-fold symmetry going on in the patterns these tiles produce. Indeed, if you ignore the whole Penrose tiling aspect and just use them as a construction polypanel, they play rather nicely with pentagons.
For yet another polypanel rhombus that also has interesting properties, check out my "Root Two Rhombus Polypanel".
I've added a second version of each rhombus which I think improves the visual effect of the tiling pattern. I found the gaps around the connectors in the original design were distracting away from the pattern the tiles produced.
The new rhombus versions invert the design so that the hollow parts of the old versions are now solid and the solid parts are now hollow. The new versions also close most of the gaps around the connectors by adding small wings that extend outward from the base at a 45 degree angle. They need to be angled like this so as not to interfere with the polypanels being used in 3D construction models, but they still print just fine without supports.
Note that you don't need as many of the thinner rhombuses as the wider ones to tile the plane so I would recommend printing them out in a ratio of about 2 thinner ones for every 3 wider ones.
Following a suggestion by @Duduche, I've added a third version of the rhombuses for people who are far more interested in Penrose tiling than polypanels. These rhombuses don't have polypanel connectors but can instead be joined like a regular jigsaw puzzle, and without the gaps that the polypanel connectors otherwise introduce. The shapes protruding from the edges of these two new tiles are like keys that only fit edges that correctly continue the pattern of curves and dots. However, this won't stop you arranging the tiles incorrectly to produce a gap that no tiles can possibly fit into.
These two rhombuses are completely flat so could be made using a laser cutter instead of a 3D printer. I don't have experience preparing DXF files for laser cutters so I've also included my original Fusion 360 files (.f3d) for anyone who wants to play around with them and generate DXF files. These f3d files have parameters set up so you can adjust the edge_length, thickness and tolerance values by selecting 'Change Parameters' from the 'Modify' menu in Fusion 360. Note that the tiles shown in the photo for this version (Version 3) were 3D-printed rather than laser cut.