This invention relates to the building art, and more particularly to blocks for the construction of buildings, structures, and hardscaping items, and to a method for assembling building blocks without using mortar. A building block, configured as a parallelepiped, comprises three pairs of opposing faces, including four lateral faces and two faces constituting an upper and a lower bases, each of the faces including a plurality of elements constituting projections and recesses, wherein each of the elements is shaped as a regular pyramid with rounded edges, and the pyramid vertex angle between two opposing faces is within the range from 90 to 179.9 degrees. The projections and recesses are arranged in rows and columns, wherein the pyramid bases at each of the parallelepiped faces are arranged in a single plane which is a face of the parallelepiped, and the respective sides of the pyramid bases are parallel to the parallelepiped faces, wherein the sides of the base of a pyramid that constitutes a projection are adjacent to the respective sides of the bases of adjoining pyramids that constitute the recesses. Projections and recesses at the block faces enable coupling of four blocks, three of which having paired adjacent faces that are perpendicular to each other and in contact at the edges. Also described are various embodiments of the block and of a method for assembling building blocks.