The most common depiction of the compound of five cubes uses solid cubes, each of a different color:
This isn’t the only way to display this compound, though. If the faces of the cubes are hidden, then the interior structure of the compound can be seen. An edges-only depiction, still keeping a separate color for each cube, looks like this:
If these thin edges are then thickened into cylinders, that makes a third way to depict this polyhedral compound. It creates a minor problem, though: edges-as-cylinders looks awful without vertices shown as well, and the best way I have found to depict vertices, in this situation, is with spheres. With vertices shown as spheres, however, a sixth color, only for the vertex-spheres, is needed. Why? Because each vertex is shared by six edges: three from a cube of one color, and three from a second cube, of a different color.
Finally, here are all three versions, side-by-side for comparison, and with the motion stopped.
All images in this post were created using Stella 4d: Polyhedron Navigator, software you may try for free at this website.
This has an amazing structure. You can see the star points and pentagons. It seems so unnatural to combine 5 cubes, i.e. 5 doesn’t seem to have much in common with 8 corners, 6 faces, and 12 edges. But the dodecahedron has 12 sides, 30 faces, and 20 corners, to match up with the 6 and 12 of the cube. Kind of like geometric factoring. It’s cool. 🙂
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Such a GLORIOUSLY, BEAUTIFUL composition. Discovering this has been a delightful secret on which I can now gaze upon anytime I want as a wondrous point of geometric joy.
Clarity in a world awash with emotion and the beings ruled by them.
It’s also really awesome, to discover another, who also dreams in geometry.
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