This feels overly verbose. I've heard following interpretation:

* 3-dimenional space is equivalent of our world.
* 4-dimension is a line where each point is equivalent of 3-dimensional world.
* 5-dimensional space is a plane where each point is an equivalent of 3-dimensional world
* 6-dimensional space is a 3d space where each point is an equivalent of our 3-dimensional world.

Would you say this interpretation is correct?
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