Why are three-dimensional organisms composed of two-dimensional layers?

Multicellular organisms are ensembles of quasi-two-dimensional structures (sheets) of various kinds. Why should the development of all organisms be mediated by a quasi-two-dimensional structure? Why does such development avoid a direct confrontation with the third dimension? In this paper, we accept the challenge of addressing this question from the perspective of computational geometry and suggest that the construction of three-dimensional organisms may be explained by the constraints imposed on a bottom-up construction process.