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A rep-tile is labelled rep-n if the dissection uses n copies. Such a shape necessarily forms the prototile for a tiling of the plane, in many cases an aperiodic tiling. A rep-tile dissection using different sizes of the original shape is called an irregular rep-tile or irreptile. If the dissection uses n copies, the shape is said to be irrep-n ...
Sierpiński demonstrated that his carpet is a universal plane curve. [3] That is: the Sierpiński carpet is a compact subset of the plane with Lebesgue covering dimension 1, and every subset of the plane with these properties is homeomorphic to some subset of the Sierpiński carpet.
From a Wythoff construction there are ten hyperbolic uniform tilings that can be based from the regular octagonal and order-8 triangular tilings.. Drawing the tiles colored as red on the original faces, yellow at the original vertices, and blue along the original edges, there are 10 forms.
Russia is pulling back its military from the front lines in northern Syria and from posts in the Alawite Mountains but is not leaving its two main bases in the country after the fall of President ...
The matching rules force a particular substitution: the two A L tiles in a φ A L tile must form a kite, and thus a kite decomposes into two kites and a two half-darts, and a dart decomposes into a kite and two half-darts. [45] [46] Enlarged φ B-tiles decompose into B-tiles in a similar way (via φ A-tiles).
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