Planigon

In <a href="/facts/Geometry/wTQf5ffQ">geometry</a>, a planigon is a <a href="/facts/Convex_polygon/7x35w610">convex polygon</a> that can fill the plane with only copies of itself (<a href="/facts/Homotopy/1nWrPxdj">isotopic</a> to the <a href="/facts/Prototile/zh5RBHy5">fundamental units</a> of <a href="/facts/Monohedral_tiling/7BWDywXC">monohedral tessellations</a>). In the Euclidean plane there are 3 regular planigons; <a href="/facts/Equilateral_triangle/MJomsYDS">equilateral triangle</a>, <a href="/facts/Square/JHJeMvmL">squares</a>, and <a href="/facts/Regular_hexagon/DPzuCzWE">regular hexagons</a>; and 8 <a href="/facts/List_of_Euclidean_uniform_tilings/c1ALUDMm">semiregular</a> planigons; and 4 <a href="/facts/Euclidean_tilings_by_convex_regular_polygons/tR5CQACy">demiregular</a> planigons which can tile the plane only with other planigons.
All angles of a planigon are whole divisors of 360°. Tilings are made by edge-to-edge connections by perpendicular bisectors of the edges of the original uniform lattice, or centroids along common edges (they coincide).
Tilings made from planigons can be seen as <a href="/facts/Dual_polyhedron/rkIHbmAf">dual tilings</a> to the <a href="/facts/List_of_Euclidean_uniform_tilings/c1ALUDMm">regular, semiregular</a>, and <a href="/facts/Euclidean_tilings_by_convex_regular_polygons/tR5CQACy">demiregular</a> tilings of the plane by <a href="/facts/Regular_polygon/ws89Nhpt">regular polygons</a>.

Planigon open-in-new

Planigon