Lesson plan
Planigon
s, eight planigons, four demiregular planigons, and six not usable planigon triangles which cannot take part in dual uniform tilings; all to scale. In geometry, a planigon is a convex polygon that can fill the plane with only copies of itself (isotopic to the fundamental units of monohedral tessellations). In the Euclidean plane there are 3 regular planigons; equilateral triangle, squares, and regular hexagons; and 8 semiregular planigons; and 4 demiregular 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 dual tilings to the regular, semiregular, and demiregular tilings of the plane by regular polygons.
Article summary
s, eight planigons, four demiregular planigons, and six not usable planigon triangles which cannot take part in dual uniform tilings; all to scale. In geometry, a planigon is a convex polygon that can fill the plane with only copies of itself (isotopic to the fundamental units of monohedral tessellations). In the Euclidean plane there are 3 regular planigons; equilateral triangle, squares, and regular hexagons; and 8 semiregular planigons; and 4 demiregular 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 dual tilings to the regular, semiregular, and demiregular tilings of the plane by regular polygons.
Key claims
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.