I have a 6-sided equilateral polyhedral cone in $R^3$ defined by a symmetric set of equations:
$C=\{(X_1,X_2,X_3)\ |\ K X_i\leq X_j \forall i,j\in\{1,2,3\}\}$
Given an point $P=(P_1,P_2,P_3)$, I would like to know what is the closest point on the cone to $P$.
I will need to implement this as an algorithm, so the more elegant a solution the better.