In this talk, we discuss how molecular geometry can be reformulated through higher-dimensional geometric models, with particular emphasis on homogeneous and conformal representations. Starting from the classical Euclidean description of three-dimensional molecular space, we show how the introduction of a single additional coordinate leads to a homogeneous framework in which isometries in 3D space admit a matrix representation in 4D space. Building on this idea, we then consider the conformal model, where one further dimension is introduced, yielding a five-dimensional representation in which rigid motions in 3D space can be realized as orthogonal transformations in 5D space. Within this setting, interatomic distances and their derivatives with respect to internal molecular coordinates can be expressed in a compact and geometrically meaningful form. The talk will highlight how these representations provide not only an elegant theoretical framework, but also potential computational advantages for molecular modeling, especially in problems where distance constraints and internal coordinates play a central role.