Three Different Depictions of the Compound of Five Cubes

The most common depiction of the compound of five cubes uses solid cubes, each of a different color:

Cubes 5

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:

Cubes 5 edges

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.

Cubes 5 thick edges

Finally, here are all three versions, side-by-side for comparison, and with the motion stopped.

cover

All images in this post were created using Stella 4d: Polyhedron Navigator, software you may try for free at this website.

About RobertLovesPi

I go by RobertLovesPi on-line, and am interested in many things. The majority of these things are geometrical. Welcome to my little slice of the Internet. The viewpoints and opinions expressed on this website are my own. They should not be confused with the views of my employer, nor any other organization, nor institution, of any kind.
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2 Responses to Three Different Depictions of the Compound of Five Cubes

  1. 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. 🙂

    Liked by 1 person

  2. Anonymous says:

    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.

    Liked by 1 person

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