Synestructics is a construction set invented by Peter Pearce and described in his wonderful book Structure in Nature is a Strategy for Design.  Ahead of its time perhaps, it was produced in the 1970's but is no longer available.  As the image shows, there are white plastic nodes and colored plastic struts.  The strut directions correspond to the axes of symmetry of the cube.  There are square orange struts along the 4-fold axes, triangular yellow struts along the 3-fold axes, and rectangular purple struts along the 2-fold axes.  The cross-section shapes of the struts match the knobs on the nodes to keep everything aligned.
The image at left shows how there are different lengths for the struts, and there are also flat panels which can create polygon faces.  A range of polyhedra can be built with Synestructics. With orange struts you can build a cube or cubical lattice.  With just purple struts you can build a regular tetrahedron, regular octahedron, truncated tetrahedron, truncated octahedron, or cuboctahedron. 
Octahedron, with triangular panels for faces