Here are a few animated illustrations that are discussed in one or more notes on this site.## Kinematics of a Hypocycloidal Engine

This applet illustrates the workings of an unconventional internal combustion engine.## 24 Electrons on a Sphere

This shows the minimum energy configuration of 24 charged particles on the surface of a sphere. The colors of the edges denote their lengths. Notice that the surface of this solid consists of 24/4 perfect squares, 24/3 perfect triangles, 24/2 additional "bi-gons", and of course 24/1 vertices, all arranged so that each vertex is identical. In addition, the vertices have a "handedness", so there are really two distinct versions of this solid.## Bell-Ringing Solid

This shape is what's called a "truncated octahedron", one of the 13 Archimedian solids. It has six square faces and eight hexagonal faces, making a total of 14 faces. The number of edges is 36, as required by Euler's formula F + V - E = 2. There is an interesting connection between this solid and the patterns of bell ringing.## Kepler's Rhombic Dodecahedron

This is one of the most fascinating of the simple solids, with an interesting correspondence to "the shape of coincidences".## The Stars In The Sky

This applet shows the positions of all 297 stars with magnitudes less than 3.5, projected onto a sphere like a planetarium. The above illustrations are discussed in the notes The Stars In The Sky Hypocycloidal Engine Min-Energy Configurations of Electrons on a Sphere Ringing of the Changes (The Shape of 4!) Meeting Probabilities and The Shape of Coincidence

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