These interconnecting “tube-like” pieces offer a tactile way to explore and discover the geometry of the 12-sided dodecahedron and 20-sided icosahedron, two dual Platonic polyhedra.
See video here: https://youtu.be/SR5kkRHFiGo
Pieces snap together at a 90-degree angle. The connecting surfaces of the “Penta Tube” align with the edges of a regular pentagon. The angles of the connecting surfaces of the “Dihedral Tube” are derived from the dihedral angle of the dodecahedron, that is, the angle between two adjacent faces of a dodecahedron. The “End Cap” is an aesthetic option for putting on unused ends.
The primary structure that can be made using these pieces is a basic dodecahedron using 12 “Penta Tubes” and 30 “Dihedral Tubes.” This is the spherical structure pictured above. The “Penta Tubes” become the faces of the dodecahedron, while the “Dihedral Tube” is oriented orthogonal to the edge of the dodecahedron and holds adjacent faces at the proper dihedral angle.
Try changing the orientation and positioning of the pieces and you’ll discover even more polyhedra based on the dodecahedron and icosahedron.