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The Robinson triangles arising in P2 tilings (by bisecting kites and darts) are called A-tiles, while those arising in the P3 tilings (by bisecting rhombs) are called B-tiles. [31] The smaller A-tile, denoted A S , is an obtuse Robinson triangle, while the larger A-tile, A L , is acute ; in contrast, a smaller B-tile, denoted B S , is an acute ...
For some tilings only one of the constructions is known to yield that tiling. Others can be constructed by all three classical methods, e.g. the Penrose tilings. [19] Goodman-Straus proved that all tilings generated by substitution rules and satisfying a technical condition can be generated through matching rules.
The puzzle proved popular, and Sulzberger himself authored a Times puzzle before the year was out. [11] In 1950, the crossword became a daily feature. That first daily puzzle was published without an author line, and as of 2001 the identity of the author of the first weekday Times crossword remained unknown. [13]
Tilings MLD from the tilings by P1 and P3, Robinson triangles, and "Starfish, ivy leaf, hex". Penrose P3 tiles: 2: E 2: 1978 [9] [10] Tilings MLD from the tilings by P1 and P2, Robinson triangles, and "Starfish, ivy leaf, hex". Binary tiles: 2: E 2: 1988 [11] [12] Although similar in shape to the P3 tiles, the tilings are not MLD from each other.
Joining puzzle fans' morning rotations of the crossword, Wordle, and Connections is Strands, the New York Times' latest puzzle. Available to play online, Strands initially looks like a word search.
Some substitution tilings are periodic, defined as having translational symmetry. Every substitution tiling (up to mild conditions) can be "enforced by matching rules"—that is, there exist a set of marked tiles that can only form exactly the substitution tilings generated by the system. The tilings by these marked tiles are necessarily aperiodic.
All three of these tilings are isogonal and monohedral. [26] A Pythagorean tiling is not an edge‑to‑edge tiling. A semi-regular (or Archimedean) tessellation uses more than one type of regular polygon in an isogonal arrangement. There are eight semi-regular tilings (or nine if the mirror-image pair of tilings counts as two). [27]
The New York Times has used video games as part of its journalistic efforts, among the first publications to do so, [13] contributing to an increase in Internet traffic; [14] In the late 1990s and early 2000s, The New York Times began offering its newspaper online, and along with it the crossword puzzles, allowing readers to solve puzzles on their computers.