Refer to the following information in doing Exercises 19–22. A particularly simple kind of polygon, called a polyomino, is made of squares joined edge-to-edge. The name is a generalization of “domino”; indeed, there is only one kind of domino (two squares joined at an edge to form a rectangle). There are just two trominos (short for “triominos”), the straight tromino and the L-tromino. The straight tromino has the shape of a rectangle, so it can tile the plane by translations; the L-tromino has the shape of a hexagon.
Question 20.51
21. Show how alternative 2 of the Translation Criterion can be applied to the L-tromino.
21.
The only way to tile by translations is to fit the outer “elbow” of one tile into the inner “elbow” of another. Labeling the corners as follows works: the corners on the top and , those on the rightmost side and , the middle of the bottom , and the middle of the leftmost side .
A-42