Thanks, I hadn't seen that response before! Fun one :)
Just draw them in seven dimensional space.
This guy fucks!
We can barely afford 5 dimensions with our current operating budget, and it's just not going to scale, I'm afraid. Saddle up boys, I'm proposing we draw them on a _hyperbolic plane_. Two dimensions, fits on a coffee table, room for as many parallel lines as we'll ever need. Hell, some of them can be ultraparallel. Plus, we can deploy it on AWS non-End User Computing for Logical Infrastructure Deployment.