The golem
This shape which I have named the golem, was hand picked from hundreds of Spectre-like polygons (Spectroids) that were sent my way via Ortwin Schenker, Bob Nungester and Bram Cohen. This golem has the same number of sides as the Spectre and also shares internal angles of 90, 120 and 270 degrees. Below left is the simplest of the periodic tilings. Positioning of new tiles is forced in most cases. That said, the pattern can deviate at any time by placing other rotations where there are choices (as shown in the example bottom right). The golem is a delight to tessellate (you can't go wrong!). Below are a few more examples of periodic tilings. These can be sewn together to make larger chaotic tilings with a bit of tweaking. Next up are a couple of radial patterns. The example on the right is (I think) quite unusual in that three golem segments are pointing towards the centre whilst the other three are pointing outwards. The golem has mirror symmetry...