A modular construction system is disclosed comprising a plurality of identical module blocks. Each module block comprises a nominally cubical shape, every face of which is a square with three unit by three unit dimensions. Located at the center of a plurality of the faces of the module block is an indentation having a square shape with one unit by one unit dimensions. Extending outward from the module block are a plurality of projections each having a square cross-sectional shape with one unit by one unit dimensions. Each projection is adapted for insertion into an indentation in the face of another module block thereby forming a constructive assembly.

A set of geometric construction pieces, units, or blocks is provided including one large central piece and four pair of decreasingly smaller pieces which can be formed together to form a nested hollow cube for storage purposes. The pieces are manually separable and may be reconfigured or rebuilt to form a plurality of different and distinct geometrical sculptural designs, patterns and structures from the pieces thereof. The set includes a large single central piece formed from six identical, elongated, rectangular legs configured as a single or integral piece forming a partial external skeleton of the nested storage cube such that each face of the cube includes only one pair of adjacent sides with the diametrically opposite face including only the opposite pair of adjacent sides so as to provide an opening into the hollow interior of the piece. A second and a third pair of structurally similar pieces, each dimensioned smaller than the other, and smaller than the single piece are identical in configuration but smaller in size so they can be nestably received within the hollow interior of the first piece. The fourth set of pieces each includes a cube having one pair of diametrically opposite corners missing and being dimensioned so as to nestably received within the third pair of units. The fifth and last pair of pieces include cubes adapted to be nestably received within the missing corners of each of said fourth pair of pieces. In this manner, each piece nests within the next larger piece until all form a hollow cube having the dimensions of the large single piece with the pieces being readily removable for constructing new different and distinct geometrical sculptural designs, patterns, models, structures, puzzles, constructions, and the like therefrom.

A puzzle piece and puzzle made from the pieces is disclosed. The puzzle piece has a center member having a first surface and a second surface, the first surface and the second surface have four long edges and four short edges. Each of the edges has a first end and a second end, and wherein a first two of the long edges meet to form an angle at one of their ends and at the other end of each of the long edges each edge meets and forms an angle with a short edge. A second two of the long edges meet to form an angle at one of their ends and at the other end of each of the long edges each edge meets and forms an angle with a short edge. Each of the short edges have a first and second end and two of the short edges meet to form an angle and the remaining two of the short edges meet to form an angle. The central member has four legs extending from each of the first and second surfaces.

A modular construction block comprising a configuration built up from five indentical rectangular sub-blocks dimensioned in the ratio of 1:2:4 and assembled into an "H"-shaped symmetric block about either of two vertical perpendicular planes through the center of the block. The assemblage provides an "H"-shaped block wherein all external dimensions, slots and recesses are integer multiples of the minimum sub-block dimension. The blocks can be assembled together in a very wide variety of combinations to create utilitarian or decorative structures. The blocks may be sized for toy construction sets or for full sized building projects. The blocks may be formed of wood, plastic, metal, concrete or ceramic depending upon size and use.

A toy block unit having a central hub and at least three attachment arms extending outwardly along non-parallel axes projecting from the central hub. At least one of the axes projects out of the plane defined by the other axes. The attachment arms are dimensioned for interconnection with identical arms on adjacent block units, to allow the construction of three-dimensional structures.