This may be a silly question, but I am curious as to what graphs generally look like in different dimensions.
If you think about it, the basic number line can be thought of as the space in $ℝ^1$, so it could be argued that a "graph" in $1D$ results in a single point.
Most of us probably know that the graph in $2D$ results in a curve in $ℝ^2$.
And a graph in $3D$ results in a surface in $ℝ^3$.
From taking multi-variable calculus, I believe a graph in $4D$ results in a solid in $ℝ^4$ but I could be mistaken there.
But I am not sure what comes after a solid for a graph in $5D$. A tesseract maybe? And of course the dimensions after that I am unsure of as well.
And is it possible to go the other way, where we go below the First Dimension? Does the idea of $0D$ or even negative dimensions exist?
So I guess my question is this: is there any sort of "hierarchy" of this sort of thing? Such as:
...->_____ ->Point -> Curve -> Surface -> Solid ->_____ ->...