@mathgrrl wrote a nice piece about her attachment to Cairo and Prismatic pentagonal tiles back in 2014 - gosh was it really 5 years ago!
and published a version here https://www.thingiverse.com/thing:338803
Here is another version of the tiles with tabs for joining them in OpenSCAD and hence customisable. The tabs have rotational symmetry around the midpoint and are scaled to the length of the side so they only constrain joining at sides of equal lengths.
The picture shows tiling constructed from laser-cut birch plywood.
As with my other recent tiling, you can adjust the inset (offset) to get a snug fit on either 3D prints or 2D laser-cuts.
The approach using perimeter definitions means that other tiles can be added: when tiling with these two tiles, it seemed that a hex tile would fit nicely and this defines one which matches the appropriate side:
function hex() =
let(r = sqrt(3)-1)