# Out there

**Discrete Mathematics**Level 5

Brilli the Ant is tripping out in 7-dimensional space (don't ask me how she got there). She recalled looking at a kaleidoscope, and seeing pretty patterns through reflections, because the pairs of lines all met at \( 60^\circ\). This led her to wonder, what is the most number of (non-parallel) lines in \( \mathbb{R}^7 \) such that the angle between **any two of them** is the same?

**Details and assumptions**

Since we're only interested in the angle between the lines, you may assume that they all pass through the origin.

The angle between 2 intersecting lines in \(n\) dimensions can be determined by just looking at the plane containing both lines.

There is no requirement that the angle must be \( 60^\circ \).