For Exercises 37–40, refer to the information about polyominos preceding Exercise 19. We saw earlier that all the dominos, trominos, and tetrominos tile the plane by translations. Here, we investigate the 12 pentominos, shown below with a letter notation for each. (If you allow mirror images to count as different pentominos, there are 18.) It will be useful for you to make several copies of each of them.
Question 20.69
39. Apply the Conway Criterion to the U-pentomino and show how it can tile by translations and halfturns.
39.
Place the U on a coordinate system with unit length for the side of a square and with the lower left corner at (0, 0). Then works.