Recreational Mathematics(5)

Together with Alda Carvalho, Jorge Nuno Silva e Ricardo Teixeira, I propose the Playing Symmetries - Sidewalks of Lisbon.

This deck is a joint project Ludus Association - University of Lisbon. The deck has problem-cards (spades and hearts) and solution-cards (clubs and diamonds). The problem-cards are as follows:

The solution-cards are as follows:

This is a deck for collectors. Each card-problem has a motif. The aim is find a place in Lisbon with the motif done in Portuguese pavement. Besides, who knows mathematics, may try to classify the symmetry.

The solution-cards show a possible place in Lisbon and the classification. Thurston notation (Orbifold notation), crystallographic notation and Tóth notation (here) are used.

In the Simetria Passo a Passo project, until 23rd June 2010, there were six wallpapers missing. We found one; see the Jack of Diamonds, fatal card in the classic movie The Cincinnati Kid.

The cards are organized by color. For example, the solution of the 10 of spades is the 10 of clubs (or the solution of the ace of hearts is the ace of diamonds).

Notice that there are exactly 7 friezes + 17 wallpapers + 2 rosetes (dihedral and cyclic), giving the total of 26 cards = 2 suits.

It seems done on purpose for a deck of cards!

In Lisbon, five wallpapers are missing. For this reason, there are five abstract problems. We decided to call these imaginary places the names of the Platonic solids. These solids were designed, of course, in strict perspective.

The deck box has an ambigram. See the following video:

Finally, there is a mirror Joker. This card is appropriate to identify simple reflections:

Lisbon is a beautiful place. Why not walk with this deck as a map? Have fun!