There are a wide variety of geometric puzzles beyond the typical picture puzzle. Some are intended to be therapeutic, some are intended for recreation and some are tests. All of them involve matching shapes -- often inverse shapes like a star-shape, into a star-shaped hole. Geometric puzzles can be two-dimensional or three-dimensional. They can be simple or complex. Adding factors like different colors and textures can create an extra layer of difficulty, because two pieces that fit geometrically may be mismatched in other ways. Adding a time constraint to a geometric puzzle is another common way to test spatial skills, or to have fun testing yourself.
Mobiles may bring to mind the hanging sculptures of Alexander Calder, or an infant's toy mobile hanging above a crib. Regardless of the type of mobile, mobiles are a complex exercise in spatial arrangement and balance. Mobiles use the concept of an adjustable teeter-totter, where a small force at the end of a long lever, can equal a relatively large force at the end of a short lever. So one teetering element can be hung from another, and another, indefinitely, in an experiment in space, balance and aesthetics.
Designing anything with modeling materials, rather than drawing it on paper, is a great spatial exercise. Instead of designing blueprints on paper to build a tree house, for example, the design for a structure can be done by stacking blocks or assembling other modeling materials. This is a helpful spatial exercise that allows you to see objects and spaces in relationship to one another. Thinking of objects' various scales is also an excellent spatial exercise.
Assembling a three-dimensional object from a two-dimensional image is another transformation that both draws upon and develops spatial skills. Building a balsa wood airplane from plans is a great example. Typically, the plans will only give you top views and side views of the model's components. But, once assembled, the profiles translate into a three-dimensional form.