In R¹ the boxes are line segments, in R² rectangles and in Rⁿ hyperrectangles.
Boxes present the advantage of being very easily manipulated by computers, as they form the heart of interval analysis.
Many interval algorithms naturally provide solutions that are regular subpavings.
[1] In computation, a well-known application of subpaving in R² is the Quadtree data structure.
In image tracing context and other applications is important to see X⁻ as topological interior, as illustrated.