The golem

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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 and fits to an underlying regular hexagon grid.  



I have found 41 unique single corona configurations.  All can continue to tile the plane in various ways, either on their own or with the addition of individual tiles.  Golems are limited to only three rotations (120° from one another) indicated by the colours.




Here's a couple of examples of single corona clusters that can be positioned around themselves to produce larger periodic tilings.  Examples top and bottom have translational symmetry.  Even though the clusters are quite different, the resulting pattern is essentially the same if the bottom example is rotated through 120 °.




Other clusters need to be rotated and mirrored which  in turn produces more complex patterns.  In this example, rotations of golems have been recoloured accordingly so that their colour always match their orientation.




Exactly the same cluster as above but golem colours remain fixed.  I have also expanded the pattern further.



Below are a couple of examples of non-tiling coronas.  The three-fold pattern can continue with either placement of individual golems or perhaps combinations of other coronas (it's that easy!).




Here's another but with two different configurations from the same corona.




Rosettes to finish.





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