In this article, we present the $n$-dimensional version of the waterpixels, namely the watervoxels. Waterpixels constitute a simple, yet efficient alternative to standard superpixel paradigms, initially developed in the field of computer vision for reducing the space cost of input images without altering the accuracy of further image processing / analysis procedures. Waterpixels were initially proposed in a 2-dimensional version. Their extension to 3-dimensions---and more generally $n$-dimensions---is however possible, in particular in the Cartesian grid. Indeed, waterpixels mainly rely on a seeded watershed transformation applied on a saliency map defined as the linear combination of a gradient map and a distance map. We propose a description of the algorithmics of watervoxels in $n$-dimensional Cartesian grids. We also discuss its parameters and its time cost. A source code for 2- and 3-dimensional versions of watervoxels is provided, such as a 2-dimensional demonstrator.