Turning and turning in the widening gyre...
William Butler Yeats, The Second Coming
The tests below constitute a series designed to assess your ability to identify whether a pair of simple, two-dimensional shapes built from squares ("polyominoes") are identical except for rotation in a plane without reflection. This is the same as asking whether one of the simple shapes can be transformed into the other by turning it on a flat surface without flipping it over.
Each test has 10 items. In each item, you will be given five pairs of shapes. Within an item, the shape on the left is the same in all five pairs, while the shapes on the right are different. The task is to select all shapes on the right that are identical to the shape on the left except for rotation in a plane without reflection. In each item, the correct answer includes at least one shape but does not include all five shapes.
These tests are an assessment either of the ability to rotate a two-dimensional object in one's mind, or to decode spatial relationships in an imagined two-dimensional space and respond to questions about those spatial relationships. In either case, these tests require some amount of spatial ability, either in the subdomain of visualization or in the subdomain of spatial relations.
The item type found in these tests or similar item types are sometimes found on professional intelligence tests. A handulf of examples comes from a battery of tests prepared by the psychologist Louis Leon Thurstone. The relevant tests by Thurstone do not involve polyominoes but instead involve other simple, geometric shapes.