|How are tessellations used in roofing, tiles, and quilts?
Tessellation is the covering of a surface without gaps or overlaps using one or a small number of basic shapes. It's a natural activity for roofers, tilers, and quilters, since those activities involve forming complete surfaces with a limited number of shapes. Since there are an infinite number of possible tessellations, people are always trying to create interesting new ones. You can find these in a tile catalog or a quilting guide. Tessellations appear in physics in the context of crystal structure, where surfaces and volumes must be filled completely with a few basic molecular arrangements. Quasicrystalline materials—materials with orientational order but no longer-range order—are a particularly interesting example of tessellation in physics.