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2. Cairo pentagonal tiling - Wikipedia

   en.wikipedia.org/wiki/Cairo_pentagonal_tiling

   The union of all edges of a Cairo tiling is the same as the union of two tilings of the plane by hexagons.Each hexagon of one tiling surrounds two vertices of the other tiling, and is divided by the hexagons of the other tiling into four of the pentagons in the Cairo tiling. [4]

3. Knot density - Wikipedia

   en.wikipedia.org/wiki/Knot_density

   A carpet with a lesser knot density is better adapted to bold, geometric designs and can utilize a long pile for softer, more reflective surface that appeals to the sense of touch." [9] Hand-tying of knots is a very labour-intensive task. An average weaver can tie almost 10,000 knots per day. More difficult patterns with an above-average knot ...

4. Sierpiński carpet - Wikipedia

   en.wikipedia.org/wiki/Sierpiński_carpet

   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.

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6. Order-8 triangular tiling - Wikipedia

   en.wikipedia.org/wiki/Order-8_triangular_tiling

   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.

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