Penrose Tiling Exploration

Objective: Study tessellations by Penrose tiles and other aperiodic sets.

Materials

• Set of Penrose tiles

Procedure

1. Ignore the matching rules and use the Penrose tiles to make a periodic tessellation.
2. Make a tessellation using the tiles and following the matching rules.
3. There are seven possible ways to fit the Penrose tiles around a single point (a vertex). For example, this configuration is called the 'Ace': . Find and draw all seven possibilities (or as many as you can find).
4. David Austin has two applets to make tessellations using the Penrose rhombs. Try with the first applet, which provides no assistance, and then scroll down to use the second applet, which won't let you get stuck and gives hints when tiles are forced.
5. Look for Penrose tilings in the Architecture of Storey Hall at RMIT, in Melbourne.
6. Explore other aperiodic tilings at the Tilings Encyclopedia. Particularly interesting are the:
   • Ammann Chair
   • Penrose Pentagon-Boat-Star
   • Danzer's 7-fold (original)
   • Hexagonal Aperiodic Monotile

Handin: A sheet with answers to all questions.