Abstract: A block toy kit is composed of a plurality of magnetic construction units magnetically connectable to each other, wherein at least one of the units comprises a hollow block main body having at least one flat surface portion with at least one magnet holds corresponding to the plural flat surface portion, arranged on inner sides of the respective flat surface portions and having magnet holding portions extending in parallel with said corresponding flat surface portions Permanent magnets are accommodated within the magnet holding portions of said magnet holders for rotation about an imaginary “X-axis” extending at parallel relative to the flat surface portion corresponding to the magnet holding portion.