I see it as two dimensional, with traditional Lib vs Conservative on the X axis, but Statist/Libertarian on the Y.
That would place Randian Objectivists in the upper right quadrant, Hippie Libertarians in the upper left, Communists in the lower left quadrant and Fascists in the lower right.
One benefit of this construct is that when Libs trot out the claim that Obamacare is a center-right, market-based solution, you can easily back them into an admission that it’s Fascist economics...
Libertarians are lefties, it is why they can’t be conservatives.
Your graph has no quadrant for conservatives.
Logically it appears you put them in the compartment of facists, which is absurd.
Most of our government’s economic policy is fascist, rather than the more traditional left-wing varieties of socialism (and fascism is a variety of socialism.) It’s nominal private property with heavy government control, corporatism, and heavy taxation.