Solids of Translation

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Uploaded by on Feb 11, 2007

Zonohedra, which are polyhedra bounded by centrally-symmetrical polygons, can be thought of as shadows of hypercubes. And, just as we can construct an n-cube by "tracing it out" along a set of n mutually perpendicular vectors of equal magnitude, so also we can "trace out" a zonohedron by a series of translations. Several animations depict this tracing-out process.

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Film & Animation

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Uploader Comments (rufus16180339887)

  • I found myself with my jaw dropped.

  • Thanks!

  • This is one of my favorites.

  • muito obrigada Daniel! I need to return to the original code and streamline it ... it is quite a hack, as they say.

    I was just downloading lyrics and chords for Aquarela do Brasil ... such a pretty song!

  • This is amazing!!! What program was used to construct these... shadows?

  • Hey thanks. I used Mathematica to make the animation, in this case. A series of translations "trace out" a zonohedron. It would be interesting to do this in POV-Ray.--R

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