Revisit the old building toy Construx but with more versatile connectors (knots). Each connector can connect to up to 26 beams: if we imagine a connector in the center of a cube, then it can connect to all 8 vertices, the centers of all 6 faces, and the midpoints of all 12 edges. These connectors will probably be quite large.
The knobs on the connector correspond to the faces of a rhombicuboctahedron or the vertices of a deltoidal icositetrahedron.
Beams will needs lengths in multiples of unity, sqrt(2), and sqrt(3). Color coding will probably be useful.
Inspiration was to create a building toy based on the rhombic dodecahedral honeycomb, but there seems to be no easy way of getting those blocks to stick (maybe electromagnets). Adding beams makes it work. Other honeycombs are also possible with the beams and connectors described above: cubes, tetrahedron-octahedron.
Originally looked at K'Nex, but its connectors only have dihedral symmetry.
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