Mathematical Models: Humanizing the Polyiamonds

Little effort has been made to tile objects with the polyiamonds larger than the heptiamonds. Perhaps this is because the number of different polyiamonds quickly gets into the thousands. Bit map vector programming can easily take a subset of the larger polyiamonds ( < 50 different tiles) and tile a space. Finding polyiamond sets with under 50 members allows for a complete description of the tiling possibilities. George Sichermann has a set of 25 order 10 unitary polyiamonds. There is a set of 46 sphinx tile dominoes.  Otherwise random sets are used. Adding on tiles to the core smaller orders is useful. I have used Walter Trump’s tiling program to produce the following examples. More author’s work in this direction can be seen at the following links:

  1. C. Knecht, Magic Squares and Humanizing the Polyiamonds, https://en.wikipedia.org/wiki/User:Knecht03/sandbox;
  2. C. Knecht, The On-Line Encyclopedia of Integer Sequences, http://oeis.org/search?q=polyiamond+knecht&language=english&go=Search

Download Complete work: Craig

Below are some examples:

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Download Complete work: Craig

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