Monohedral Convex Pentagonal Tiling: Type 2

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Type 2 Convex Pentagonal Tiling

Type 2 is another one of the five types published by German mathematician Karl Reinhardt in 1918.

Condition: c = e;
B + D = 180°

Sample tile:

Primitive units: 4-tile

4-tile Primitive Unit

Tiling:

4-tile primitive unit tiling

Teaching Resources / Downloadables

Puzzles

Note how the tile is constructed in GeoGebra 2D/3D. Try playing around with it!

  1. How are the constraints applied?
  2. Does all angles \alpha give you convex tile?
  3. Does all convex tiles obtained there give you a tiling?
  4. Generate a non-convex tile. Can we tile with it too?

Extra Reading

  1. Pentagonal Tiling, Type 2 (Wikipedia)
  2. Karl Reinhardt (Wikipedia)
  3. Geogebra.org
  4. Pentagon Type 2 Tiling (Wolfram | Alpha)
  5. Interactive Demonstration of Pentagonal Tiling (Wolfram)
  6. Tiling the Plane with Congruent Pentagons – Doris Schatschneider (MAA)

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