Book suggestion in higher dimensional geometry especially regarding lines and hyper-planes in high-dimensional space

Let us assume we are in 4-dimensional space comprising 4-tuples: $(x_1,x_2,x_3,x_4)$. Let us consider a plane $\Gamma_1$ in $\mathbb{R}^4$ with the equation of $x_1=x_2=0$. And let us consider another plane $\Gamma_2$:$x_1=1, x_4=0$. The two planes do not intersect each other also they are not parallel to each other. This non-parallel and no intersection property for two planes is possible in $\mathbb{R}^4$ but not possible in $\mathbb{R}^3$. Any book suggestion containing these examples in higher dimensional geometry especially regarding lines and hyper-planes in high-dimensional space?

I suggest "An introduction to geometry of n dimensions" by Sommerville, Dover editions, which describes a lot of polytopes (analogous to polyhedrons in 3 dimensions) :

https://mathshistory.st-andrews.ac.uk/Extras/Sommerville_Geometry/

The best movie on this subject, (in English or any other language), made by three french researchers (Etienne Ghys, Arélien Alvarez and Josh Leys) : "Dimensions, a walk through mathematics" :

https://youtu.be/6cpTEPT5i0A

It starts at a very simple level, and progressively explains how to have a good vision of the fourth dimension and its polytopes.

It is also an excellent visual introduction to complex numbers, in chapter 5.