The Vapnik-Chervonenkis dimension (VC dimension) of the set of half-spaces of R^d with frontiers parallel to the axes is computed exactly. It is shown that this VC dimension is smaller than the intuitive value of d. An additional approximation using the Stirling's formula is given. This result may be used to evaluate the performance of classifiers or regressors based on dyadic partitioning of R^d for instance. Algorithms using axis-parallel cuts to partition R^d are often used to reduce the computational time of such estimators when d is large.