The classical model for the 3D space is the Euclidean vector space, where isometries are not even linear transformations. In the conformal model, whose origin comes from the work of F. Wachter, a student of Gauss, isometries are not merely linear transformations (as in classical homogeneous coordinates), but also orthogonal ones. We present a new construction of the conformal model of the 3D space and explain how new insights to Distance Geometry can be gained, based on the geometric meaning of the inner product defined in the conformal model that does not satisfy anymore the positivity