Visualizing fractional geometry

I am a visual thinker. Taking intelligence tests with a grain of salt, in 9th grade I was given a multiple intelligences I/Q test and the results indicated that my visual-spatial intelligence was a full 20 points higher than my intelligences in other areas. Things just make sense when you can visualize them.

Geometry itself is easy enough to visualize up to 3 dimensions, but how do you visualize something that lives in 2.5 dimensions?

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