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!
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°
Primitive units: 4-tile
Teaching Resources / Downloadables
Note how the tile is constructed in GeoGebra 2D/3D. Try playing around with it!
- How are the constraints applied?
- Does all angles give you convex tile?
- Does all convex tiles obtained there give you a tiling?
- Generate a non-convex tile. Can we tile with it too?
- Pentagonal Tiling, Type 2 (Wikipedia)
- Karl Reinhardt (Wikipedia)
- Pentagon Type 2 Tiling (Wolfram | Alpha)
- Interactive Demonstration of Pentagonal Tiling (Wolfram)
- Tiling the Plane with Congruent Pentagons – Doris Schatschneider (MAA)