6-具有双菱形项的重拟周期镶嵌
6-Fold Quasiperiodic Tilings With Two Diamond Shapes
摘要：
用于覆盖表面的一组瓦片由两种类型的瓦片组成。它们中的每一个的基本形状都是菱形或菱形，都有60度和120度的角度。它们通过将一个标记为具有60度的底角的锐角钻石，另一个标记为具有120度的底角的钝角钻石来区分。这两种类型的瓷砖可以用箭头、凹口或彩色线条标记，以保持它们的区别。凹口可以用作匹配规则，使得锐角菱形可以在其他匹配中形成具有6重旋转对称性的星形。类似地，三个钝角菱形可以与3重旋转对称匹配以形成六边形以及其他可能性。公开了非周期性膨胀方案的两种变型，以将九个瓦片匹配成两个较大的瓦片。第二代的这两个较大的图块是遵循与原始图块相同的匹配规则的新基础形状。因此，暴胀可以无限重复，产生一个任意大的表面，覆盖着一个6倍的准周期瓷砖，只包括两个钻石形状。瓷砖的缺口可以创造性地变形，使土方工程式的数字。
英文摘要：
A set of tiles for covering a surface is composed of two types of tiles. The base shape of each one of them is a diamond or rhombus, both with angles 60 and 120 degrees. They are distinguished by labeling one as an acute diamond with a base angle of 60 degrees, the other one as an obtuse diamond with a base angle of 120 degrees. The two types of tiles can be marked with arrows, notches, or colored lines to keep them distinct. Notches can be used as matching rules such that the acute diamonds can form a star with 6-fold rotational symmetry among other matches. Similarly, three obtuse diamonds can be matched with 3-fold rotational symmetry to form a hexagon among other possibilities. Two variations of an aperiodic inflation scheme are disclosed to match nine tiles into two larger tiles. These two larger tiles of the second generation are the new base shapes following the same matching rules as the original tiles. The inflation can thus be repeated indefinitely creating an arbitrarily large surface covered with a 6-fold quasiperiodic tiling consisting of only two diamond shapes. The notches of the tiles can be creatively deformed to make Escher-esque figures.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
