Summary: We study the capillary rise of viscous liquids into sharp corners formed by two surfaces whose geometry is described by power laws \(h_i(x) = c_i x^n\), \(i = 1, 2\), where \(c_2 > c_1\) for \(n \geq 1\). Prior investigations of capillary rise in sharp corners have shown that the meniscus altitude increases with time as \(t^{1/3}\), a result that is universal, i.e. applies to all corner geometries. The universality of the phenomenon of capillary rise in sharp corners is revisited in this work through the analysis of a partial differential equation for the evolution of a liquid column rising into power-law-shaped corners, which is derived using lubrication theory. Despite the lack of geometric similarity of the liquid column cross-section for \(n > 1\), there exist a scaling and a similarity transformation that are independent of \(c_i\) and \(n\), which gives rise to the universal \(t^{1/3}\) power law for capillary rise. However, the prefactor, which corresponds to the tip altitude of the self-similar solution, is a function of \(n\), and it is shown to be bounded and monotonically decreasing as \(n\to\infty\). Accordingly, the profile of the interface radius as a function of altitude is also independent of \(c_i\) and exhibits slight variations with \(n\). Theoretical results are compared against experimental measurements of the time evolution of the tip altitude and of profiles of the interface radius as a function of altitude.