Modular building blocks and building system

A modular structural building block, including

• a pair of outside walls separated by and enclosing an internal region;
• a plurality of iterated interlocking equilateral triangular structures disposed between and coupled to each of the outside walls;
• each triangular structure including one or more internal walls disposed between the outside walls and dividing the internal space into one or more internal subregions, the triangular structures alternating in opposite orientations;
• each triangular structure including a first wall having a protrusion at a vertical offset above at least a portion of the outside walls, and including a second wall having a recess at a vertical offset depressed below at least a portion of the outside walls, the protrusions/recesses each being disposed on an internal wall and including a base having a vertical offset and a pair of sides slanted and rising/falling with respect to its internal wall, the protrusions/recesses alternating in orientation, the protrusions/recesses each being disposed at an acute angle with respect to the outside walls;
• wherein the vertical offsets are disposed to match those of a second block, so that when the second block is disposed parallel to the outside walls the vertical offsets match those of the second block at the acute angle with respect to the outside walls and the landings match those of the second block;
• whereby the block is disposed to fit into a rigid structure when its protrusions/recesses match that of the second block, wherein the protrusions/recesses are disposed so that rotations about the block about at least two axes still allow the protrusions/recesses to fit together with at most one rotation of one said block.