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As someone who has a very vivid imagination - daydreaming is second nature to me. It’s very useful to me because I can use it to learn stuff by doing my best to simulate how they work step by step, usually all I need is a good description and some background info.

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How much of that imagination is real? For example, can you intersect two dodecahedrons at some random angle and see the outline of the polygon where they intersect?

Perhaps you meant to use "accurate" instead of "real"?

"Fake" would be a better word. It's easy to convince yourself that you can imagine a tree, but try to inspect it, count leafs on each branch, and you quickly realise that all those leafs are generated on the fly, and what you're really imagining is a very poor sketch of a tree.

That very much depends on the individual's visual capacity. Some can imagine very detailed images. I'd guess your right about most people though, but not all. Temple Grandin has written on what it's like to be a visual thinker. She compares her mental visualization to the Star Trek holodeck. Language is secondary to her. Something she has to translate pictures back and forth to in order to understand words.

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