A magnetic construction system comprised of plural multi-shaped structural bodies each containing one or more captured magnets, wherein each magnet is free to rotate within its respective retaining pocket to align in magnetic polarity with rotatable magnets in adjacent structural bodies. Surface geometry around each magnet may include a radial detent feature which provides lateral and rotational stability between magnetically coupled structural bodies, or a radial recess which allows free rotation of respective structural bodies about the polar axis of magnetic coupling.