Magnetic and electronic toy construction systems and elements are provided that include an assembly of at least two panels that have at least three magnets located around the perimeter of the panel such that the dipole axes of magnets in a single panel are coplanar and intersect to define a polygon. When attaching two adjacent panels, at least two ferromagnetic spheres are used such that the dipole axes of one magnet from each of the adjacent panels are collinear, and such that the dipole axes are collinear with the centers of the ferromagnetic spheres. In this manner, several panels configured in this way may be nested together to form great varieties of constructions.