One might wonder if there is a 3-dimensional "golden rectangular solid" that is analogous to the 2-dimensional "golden rectangle" (shown below), which can be sub-divided recursively so that each left-over rectangular solid has the same proportions as the original rectangular solid. The 3D analogue to the 2D golden rectangle does indeed exist, and is depicted by this application.
Choose from one of the preset application modes, or feel free to experiment.
When you've constructed one of these solids explicity, you can rotate the object around and zoom in/out with the mouse, using click-drag and two-button-click-drag movements. Instructions aren't provided, but feel free to contact me with any questions.
See the help file for a more complete description of the stand-alone application.
Screenshot:
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