Abstract We discuss the embedding of point/line configurations into projective space over a field. These embeddings are not always faithful, and may have extra induced subspaces. A heuristic condition is found that depends upon an invariant called freedom . Algorithmic methods that implement an embedding are discussed. For example, drawing a k 3 -configuration in a plane boils down to ordering the vertices of an associated cubic graph. Every connected k 3 -configuration can be described by a single algebraic equation, that can be solved to obtain every planar embedding. These planar embeddings can then be “lifted” to obtain all higher dimensional embeddings.