Summary

A sphere with spiral voids for spring segments.
The voids are mutually orthogonal, so the spheres, when connected with springs, make a cubic arrangement in space.
The masses and springs react to touch with vibrations, and to vibrations with resonances, modeling phonons.

Instructions

The sphere is printed in white PLA on a M'bot Rep'2, 2 shells, 20%fill. Weighs about 28 g, prints in 2hr18m.
The mass and spring cubic crystal model is made by taking n cubed spheres, and connecting them with segments of spring.
The connector is seven turns cut from (Long Type 302 SS Extension Spring 11.0" Length, .750" OD, .047" Wire Diameter[MacMaster-Carr]) which has been overstretched to a pitch of 1cm.
This involves clamping one end of the extension spring in a vise, over-extending and relaxing it, pulling it out successively and building up to the 1 cm pitch. Don't try to pull all in one go. Relaxing involves rotation. Beware the wire loop as a handle, rather grab several coils which will go un-stretched but provide a better grip. Clamp well, stay out of the path of the spring should it let go, and don't let go of the spring when stretched.
Once the spring is stretched, segments cut with Xuron Hard Wire Shear Cutter.
Prepare the spheres by making sure the springs thread all the way into the spiral voids. Note that the three dotted sides are two turns in, and the sides, two plain and one with hole, are one turn in. The turns start 90° before going internal, so the one turn side holds 3/4's of a turn inside. All spheres should be checked and passed before gluing.
To make the cube, all of the spheres must be oriented the same way. Start gluing springs into spheres. A blob of gel cyanoacrylate on the external arc, turn the spring all the way in on the one turn side, and to the same depth (3/4's of a turn hidden) on the two turn side. At some point in the construction, two spheres are constrained in their motion, and can be connected by turning the spring all the way into the two turn hole, and then back out one turn into the facing sphere. The springs are glued in with gel cyanoacrylate. Good ventilation and nitrile gloves are necessary, a lot of crazy glue everywhere with care.

Cubic Sphere