# Complexity of merging two convex hulls in $\mathbb{R}^d$

Given two convex hulls $$C_1, C_2$$ in $$\mathbb{R}^2$$ or $$\mathbb{R}^3$$, it is known how to merge the two convex hulls into a a third convex hull $$C$$ (the convex hull of the points in $$C_1, C_2$$) in time $$O(|C_1|+|C_2|)$$ (Where $$|C_i|$$ is the number of vertices + faces of the convex hull polytope).

For constant $$d\geq 4$$, what is known on the complexity of merging two convex hulls in $$\mathbb{R}^d$$?