Technically, our cat cube is a rectangle, but it is square on each end.
It is an all-weather cat bed. In the winter, we (or whichever one one of us claims dibs) can sleep inside it, where it is nice and toasty.
Binga discovered the summer version of it by accident, when she squished it.
It folds down when the weather is warm so we can enjoy the fresh air! So in the summer, the ends are only half-square.