# How to draw six lines in 3-d space such that angle between any pair of them is the same.

My boss claimed earlier today that its possible to draw 6 lines in 3-d space, all passing through the origin such that the angle between any pair of them is the same as that between any other pair.

As an example, the 3-d coordinate system with $$x$$, $$y$$ and $$z$$ axes is such a system with three lines where the angle between any pair is $$\frac{\pi}{2}$$.

I can't imagine what a picture like this (with the $$6$$ lines) would look like. Can anyone provide insight into this?

He also said this was an application of linear algebra.