Tessellations: Geometry and Art
Tessellations are the perfect puzzle for geometry enthusiasts. They're all about creating beautiful patterns with shapes that fit snugly together, leaving no gaps or overlaps. You can spot them in everyday places, like your bathroom tiles, wallpapers, and even your cozy paper towels.
In the world of tessellations, there is one simple rule: no shape is more special than the others. They all have to blend in and continue their pattern endless. So, there are no unique shapes or lines.
While any polygon be part of a tessellation, not all of them can shine on their own. It's not about the number of sides; it's about making sure the angles add up just right. Only triangles, squares, and hexagons are able to be part of a tessellation.
Circles, for example, can't be used on their own, but they can be part of the group by filling the gaps between shapes.
Primary Tessellation Types
These are composed of identical regular polygons with matching sizes and shapes.
These tessellations are crafted by combining multiple regular polygons. Only eight specific combinations of regular polygons can create semi-regular tessellations.
Irregular tessellations consist of figures that do not involve regular polygons but can interlock without any gaps or overlaps. The possibilities for irregular tessellations are virtually limitless.
Tessellations have played a prominent role in the realms of art and architecture across various historical periods, from the intricate mosaics of Ancient Rome to the contemporary designs famously associated with artists like M.C. Escher.