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2. Tilings and patterns - Wikipedia

   en.wikipedia.org/wiki/Tilings_and_patterns

   The last five chapters survey a variety of advanced topics in tiling theory: colored patterns and tilings, polygonal tilings, aperiodic tilings, Wang tiles, and tilings with unusual kinds of tiles. Each chapter open with an introduction to the topic, this is followed by the detailed material of the chapter, much previously unpublished, which is ...

3. Lists of uniform tilings on the sphere, plane, and hyperbolic ...

   en.wikipedia.org/wiki/Lists_of_uniform_tilings...

   Edges exist between a generator point and its image across a mirror. Up to 3 face types exist centered on the fundamental triangle corners. Right triangle domains can have as few as 1 face type, making regular forms, while general triangles have at least 2 triangle types, leading at best to a quasiregular tiling.

4. Tiling with rectangles - Wikipedia

   en.wikipedia.org/wiki/Tiling_with_rectangles

   A tiling with rectangles is a tiling which uses rectangles as its parts. The domino tilings are tilings with rectangles of 1 × 2 side ratio. The tilings with straight polyominoes of shapes such as 1 × 3, 1 × 4 and tilings with polyominoes of shapes such as 2 × 3 fall also into this category.

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   Explore More: 6 Easy and Affordable Home Renovation Tips From Joanna Gaines. ... redoing the tile or adding a fresh vanity — rather than gutting the whole space unless it’s in rough shape.” ...

6. Tessellation - Wikipedia

   en.wikipedia.org/wiki/Tessellation

   The familiar "brick wall" tiling is not edge-to-edge because the long side of each rectangular brick is shared with two bordering bricks. [18] A normal tiling is a tessellation for which every tile is topologically equivalent to a disk, the intersection of any two tiles is a connected set or the empty set, and all tiles are uniformly bounded ...

7. Pentagonal tiling - Wikipedia

   en.wikipedia.org/wiki/Pentagonal_tiling

   An example is the sphinx tiling, a periodic tiling formed by a pentagonal rep-tile. [20] The sphinx may also tile the plane periodically, by fitting two sphinx tiles together to form a parallelogram and then tiling the plane by translation of this parallelogram, [ 20 ] a pattern that can be extended to any non-convex pentagon that has two ...

8. Uniform tiling - Wikipedia

   en.wikipedia.org/wiki/Uniform_tiling

   If a tiling made of 2 apeirogons is also counted, the total can be considered 39 uniform tilings. In 1981, Grünbaum, Miller, and Shephard, in their paper Uniform Tilings with Hollow Tiles, list 25 tilings using the first two expansions and 28 more when the third is added (making 53 using Coxeter et al.'s definition). When the fourth is added ...

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