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.
It's known:
Take icosahedron and 6 pairs of opposite vertices.
See also here: http://oeis.org/A002853