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Reference.org
Euclidean tilings by convex regular polygons
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Example periodic tilings<table><tbody><tr><td>A regular tiling has one type of regular face.</td><td>A semiregular or uniform tiling has one <a href="/facts/Vertex_configuration/wWaBS6t0">type of vertex</a>, but two or more types of faces.</td></tr><tr><td>A k-uniform tiling has <i>k</i> types of vertices, and two or more types of regular faces.</td><td>A non-edge-to-edge tiling can have different-sized regular faces.</td></tr></tbody></table> <p>Euclidean <a href="/facts/Plane_(mathematics)/tAUtRFcn">plane</a> <a href="/facts/Tessellation/7BWDywXC">tilings</a> by convex <a href="/facts/Regular_polygon/ws89Nhpt">regular polygons</a> have been widely used since antiquity. The first systematic mathematical treatment was that of <a href="/facts/Johannes_Kepler/wk6GTN3C">Kepler</a> in his <i><a href="/facts/Harmonices_Mundi/BDKcKU7Y">Harmonices Mundi</a></i> (<a href="/facts/Latin_language/pM3Kge85">Latin</a>: <i>The Harmony of the World</i>, 1619). </p>