Yes, there are such things as square watermelons. You can buy them in Japan supermarkets, that is if you can afford them. They cost US$80 for a pop!

The innovative idea came from a farmer from Zentsuji in Kagawa prefecture 20 or so years ago. He thought of making a cube-shaped watermelon which could easily be packed and stored. What he did is insert the melons into square, tempered glass cases while the fruit is still growing on the vine and voila, a square watermelon that won't roll over while being sliced and won't take too much space in the ref.

However, the square watermelons are sold in a selection of department stores and high-end supermarkets only as they appeal mainly to the wealthy and fashion-conscious of Tokyo and Osaka, Japan's two major cities.