Abstract: A building block assembly includes a plurality of prismatic building blocks, each of which has at least one substantially rectangular face portion in which a pair of substantially mutually orthogonal intersecting grooves are formed and a plurality of connecting elements for interconnecting the blocks. At least some of the connecting elements comprise a pair of intersecting connecting portions which define a substantially cross-shaped configuration, each of the connecting portions having a substantially S-shaped configuration having a depth greater than the width of the grooves while the thickness of the connecting portions is less than the width of the grooves formed in the block face portions.