Gusset Block Construction deals with a block that is cored from all sides. The blocks are cubes and elongated cubes with a pyramid or elongated pyramid shaped cavity on each side resulting in a block in which each of the twelve edges is central on a gusset shape extending from said edge to the central axis of the block. With the use of a second octahedron block that fits within the pyramid shaped cavities a wall that requires no fastening can be built by placing octahedrons in the top cavities of a layer of blocks and placing another layer of blocks on it. These blocks will be able to come apart at the joints during an earthquake without completely disassembling and can return to original position when the earthquake stops. They can be molded in a two piece split mold and are scaleable; tapered piers could be made.