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### Special Topics:Tilings

Tilings have been known since ancient times. There are regular tilings of the plane using squares or hexagons (like the tiles on your bathroom floor), or the regular patterns of bricks on a wall. There are also more complex tiling patterns that do not repeat themselves. Tilings are closely related to symmetries, and are often studied together. The tilings of three-space have been studied by crystalographers, and are the subject of current research into quasicrystals.

Images:

1. An aperiodic tiling
2. Aperiodic Puzzle I
3. Aperiodic Puzzle II
4. Arbitrary substitution tiling
1. 2. 3. 4.
1. DodecaFoam! First Stellation
2. DodecaFoam! Second Stellation
3. DodecaFoam! Third Stellation
4. DodecaFoam!
1. 2. 3. 4.
1. Lord Kelvin's Conjecture Disproved (I)
2. Lord Kelvin's Conjecture Disproved (II)
3. Museum Mathematics: Plane
4. Museum Mathematics: Platonic and Archimedean Solids
1. 2. 3. 4.
1. Museum Mathematics: Polyhedron
2. Penrose by Quasitiler
3. Threebolites (smooth)
4. Threebolites I
1. 2.
1. Threebolites II
2. Threebolites III