Rotate the cube 360 degrees.
Drag the horizon out of bounds.
Simple occlusion for both the faces and perspective lines.
I found Voracova's worksheet on linear perspective instructive:
[url]http://www.geogebratube.org/material/show/id/17338[/url]
For the base construction, I took the same approach.
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Worksheet 1 of (meow?)
[b]1. Linear Perspective[/b]
2. Line of sight on a sphere (circle): [url]http://www.geogebratube.org/material/show/id/33777[/url]
These are my self-study materials. Let me know how I can make them more useful to you.