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Is there any list of or a research of recommended 2D (or eventually 3D) shapes that should be used in psychology test stimuli? For example, circle, square, triangle, star, oval, rectangle etc.

For example, I would like to create a cognitive test with multiple elements. I will pick a circle, a square, a triangle and an oval. However, an oval has some properties similar to the circle and that can possibly lead to some distortion in the data. Do you know of any research that has addressed this issue? Or do you know of any list of recommended shapes?

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There is no general answer to your question. The shapes you want to use depend on what you want to study. For example, personality test correlate a preference for certain shapes (e.g. round versus angular) with specific personality traits (e.g. aggressive). If you just need distinct shapes, then your choice will depend on how distinct an two shapes are from each other. And so on. So what do you want to study? –  what Jun 18 at 6:49

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If your goal is to find a set of shapes that are unique and easily distinguishable from each other, you might be interested in stimuli that get used in visual statistical learning experiments (e.g. Fiser & Aslin, 2002; Turk-Browne, Junge, & Scholl, 2005). The same set of shapes tends to get used across multiple studies in this literature. Some examples of these shapes:

There is a repository of some of these shapes on GitHub. You can download the images there.

Note that there hasn't been research on these shapes, just that they are commonly used shapes in the literature when arbitrary 2D shapes are needed. It is likely that some pairs of these shapes are more similar than others, but since there are a couple dozen different shapes, you may be able to control for that by randomly selecting a different subset of the shapes for each subject in the experiment.

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