User blog:Ynought/Q function and a variant of grahams number

We all know grahams number and its definition.So i thought i could make a similar problem with a function that grows way faster.Defining \(Q_k\) where \(k\in mathbb{N}_+\):

The output of \(Q_k\) is \(n\) where \(n\<9 is the number of dimensions needed such that a analog of a regular \(k\)-agon in \(n\) dimensions with all vertices connected with lines colorable with \(k\) colors can not have a 2d-\(k\)-agon of lines in the same color in the same plane