This is a part of the series of posts introducing an active research field called Tessellation – The Mathematics of Tiling, discussing some basic, intuitive tiling patterns. Subscribe now (link) to get notified about more posts in coming days!

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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

Tiling:

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 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)