![\"tetra-penta-star\"](\"https:\/\/puzzlezapper.com\/blog\/wp-content\/uploads\/2013\/09\/tetra-penta-star.gif\")
<\/a><\/p>\nBut that was just the beginning! He then proceeded to produce an entire collection<\/a> of tilings with these pieces, which he calls flexominoes. One problem that can come up in tilings of this sort is that if there is a vertex with three rhombi around it, a polyomino containing all three rhombi has an ambiguous identity, since there is more than one way to “unglue” the polyomino at that point. I contributed an ambiguity-free solution to one of the patterns Abaroth found:<\/p>\n Speaking of rhombuses, Abaroth has been investigating<\/a> color-matching puzzles using rhombic tiles. His puzzle page<\/a> has more interesting material on color matching puzzles and symmetrical polyhex tilings.<\/p>\n Next up, George Sicherman sent in a symmetrical tiling for the flexible tetrarhombs:<\/p>\n What’s interesting here is that although the outline of the tiling is symmetrical, the pattern of the cells isn’t. The lesson here is that being able to trade off some cell-level symmetry for more pattern-outline symmetry can give us a little variety in our choices of what we can tile.<\/p>\n Finally, Bryce Herdt provided a de Bruijn sequence of invertible length 5 binary words. (That is, a cyclic sequence where each word occurs once as a substring.) Since he did so in text format, I made a visualization:<\/p>\n I’ve had a few solutions sent in recently, so I wanted to share them with you all. First, Abaroth noticed that my rhombic-cell pentomino tiling had just enough space to fill out into a five pointed star if the tetrominoes were also included: But that was just the beginning! He then proceeded to produce an … Continue reading Some Contributed Solutions<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[101,127,128,10,71,33],"class_list":["post-321","post","type-post","status-publish","format-standard","hentry","category-recreational-mathematics","tag-de-bruijn-sequences","tag-flexible-polyrhombs","tag-flexominoes","tag-pentominoes","tag-symmetry","tag-tetrominoes"],"_links":{"self":[{"href":"https:\/\/puzzlezapper.com\/blog\/wp-json\/wp\/v2\/posts\/321","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/puzzlezapper.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/puzzlezapper.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/puzzlezapper.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/puzzlezapper.com\/blog\/wp-json\/wp\/v2\/comments?post=321"}],"version-history":[{"count":3,"href":"https:\/\/puzzlezapper.com\/blog\/wp-json\/wp\/v2\/posts\/321\/revisions"}],"predecessor-version":[{"id":329,"href":"https:\/\/puzzlezapper.com\/blog\/wp-json\/wp\/v2\/posts\/321\/revisions\/329"}],"wp:attachment":[{"href":"https:\/\/puzzlezapper.com\/blog\/wp-json\/wp\/v2\/media?parent=321"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/puzzlezapper.com\/blog\/wp-json\/wp\/v2\/categories?post=321"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/puzzlezapper.com\/blog\/wp-json\/wp\/v2\/tags?post=321"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}<\/a><\/p>\n<\/a><\/p>\n<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"