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2. Polyhex (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Polyhex_(mathematics)

   One example self-tiling with a pentahex. All of the polyhexes with fewer than five hexagons can form at least one regular plane tiling. In addition, the plane tilings of the dihex and straight polyhexes are invariant under 180 degrees rotation or reflection parallel or perpendicular to the long axis of the dihex (order 2 rotational and order 4 reflection symmetry), and the hexagon tiling and ...

3. Hexagonal number - Wikipedia

   en.wikipedia.org/wiki/Hexagonal_number

   Proof without words that a hexagonal number (middle column) can be rearranged as rectangular and odd-sided triangular numbers. A hexagonal number is a figurate number.The nth hexagonal number h n is the number of distinct dots in a pattern of dots consisting of the outlines of regular hexagons with sides up to n dots, when the hexagons are overlaid so that they share one vertex.

4. Edge-matching puzzle - Wikipedia

   en.wikipedia.org/wiki/Edge-matching_puzzle

   MacMahon Squares is the name given to a recreational math puzzle suggested by British mathematician Percy MacMahon, who published a treatise on edge-colouring of a variety of shapes in 1921. [4] This particular puzzle uses 24 tiles consisting of all permutations of 3 colors for the edges of a square.

5. Centered hexagonal number - Wikipedia

   en.wikipedia.org/wiki/Centered_hexagonal_number

   Centered hexagonal numbers appearing in the Catan board game: 19 land tiles, 37 total tiles. In mathematics and combinatorics, a centered hexagonal number, or hex number, [1] [2] is a centered figurate number that represents a hexagon with a dot in the center and all other dots surrounding the center dot in a hexagonal lattice.

6. Hexagonal tiling - Wikipedia

   en.wikipedia.org/wiki/Hexagonal_tiling

   Hexagonal tiling is the densest way to arrange circles in two dimensions. The honeycomb conjecture states that hexagonal tiling is the best way to divide a surface into regions of equal area with the least total perimeter.

7. Cairo pentagonal tiling - Wikipedia

   en.wikipedia.org/wiki/Cairo_pentagonal_tiling

   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] Infinitely many different pentagons can form Cairo tilings, all with the same pattern of adjacencies between tiles and with the same decomposition into hexagons, but with ...