The point-set and combinatorial models of solids are entirely consistent with each other, can be used interchangeably, relying on continuum or combinatorial properties as needed, and can be extended to "n" dimensions. The key property that facilitates this consistency is that the class of closed regular subsets of ℝ"n" coincides precisely with homogeneously "n"-dimensional topological polyhedra. Therefore, every "n"-dimensional solid may be unambiguously represented by its boundary and the boundary has the combinatorial structure of an "n−1"-dimensional polyhedron having homogeneously "n−1"-dimensional neighborhoods.