[timjver]

I think the lack of left-right symmetry was the surprising bit.

[level3]

It’s not as surprising when you realize that the problem allows reflections of the shape, removing the need for a symmetrical cover. There are lots of lopsided shapes that will barely fit on one side but leave room on the other. With an asymmetrical cover you can handle different classes of shapes with each side, while a symmetrical cover ends up overcompensating and being too “one size fits all.”