Square watermelons are watermelons grown into the shape of a cube. This is generally intended for space efficiency in small refrigerators. The practice of growing cube watermelons is popular in Japan. However, the cube watermelons are often very expensive and therefore are sold more as an ornamental novelty.
Square watermelons were intended to fit more compactly in fridges and be able to be cut more easily (without rolling). They were invented by graphic designer Tomoyuki Ono in 1978. She presented the watermelons in a gallery in Ginza, Tokyo.
Source: https://en.wikipedia.org/wiki/Square_watermelon, http://www.elledecor.com/life-culture/travel/a7819/50-best-travel-destination-fact/